SUBJECT INDEX

lOA refers to subsection lOA; 10.2 refers to the result with this number in section 10; and (15) refers to page number 15. If the first letter of a word is underlined then more information can be found where this word is listed.

Absolute continuity: in a Riesz space (21); - for Banach-valued measures (31); -, characterization for scalar measures 3.B, 6.7, Cf. 22A, 29A;

- for upper S-norms 7.20, Cf. 11.10, 15.8. uniform - of linear maps on a convex set (119-120). Absolute value: (13) Adapted maps: 2BB Adequate: cover by integrable sets (B6), Cf. (96); - cover by measurable sets (170) - field 26B; - map 28A; - partition l6A (156). (~,M)-B-adequate fields (234). Admissible: function (252); - topology (108) Algebra of sets: 6.11 Almost: compact-valued functions (178);

compact measures 37A everywhere (a.e.) (74) separably-valued functions (178)

Baire: category theorem 11.5 - functions and sets 6.16; - -, dominated (66), B.23 - -, equivalent to

an integrable function 7.18; - measurable functions 19.13 Banach lattice: 3E (36), Cf. 7.10; - with order-continuous norm 3E (36), Cf. 8.13, 9A (94) Banach space over a Banach lattice 3E (36), Cf. 8.13 Band: (18); -, characterizations 2.20, 2.21;

decomposition of Riesz 2.18, Cf. 17.3 - of *-measures 3.10, 3.11, 3E; - of diffuse, discrete, or tight measures 24C a band in a band is a band 2.24 Bauer's theory: l7A, Cf. 5.9, 10.7, 24.1 Bochner: integrable (78); - integral lOA, of a weakly compact linear map

llC, Cf. 7.22 Borel: functions and sets lB.21; - -, dominated (92), 8.23 - measurability 19.14. Borel-Cantel1i lemma: 32.5 B-continuous: measure (= B-measure) 3D, Cf. 4.11, 4.19; - part of a measure 3.11, 17.3; - integral of a field 26A-B - upper gauge BC, Cf. 9.1, 11.8; associated with a lifting 34.1 weakly - linear maps 4D, llA (116)

Caratheodory: 19.D Chain rule: 22.9

343

Character (space): of a family of functions (54); -ofL"" 20B, Cf. 34.9 Clan (= ring of sets): lB (5), Cf. 1.4, 6.1, full, ~xtension, ~ectrum; - of integrable sets 8.4 Compact and (T,M)-compact linear maps: lOB Compactness: properties of the integral lOB; - criterion for admissible topologies 10.6 - of L:( 21.11 Completeness: of a Riesz space (17); - of :FE(M) 7.9; - of 4 7.12; - of £; 20.3 Complex measures: 3.14 Conditional expectation: 29A-C; - under,jj 29.8 Conditional distribution: 36.10 Conjugate numbers: (193) Content: ,elementary lB (5); -, ,S-continuous (= a-additive) (34);

, -, extension 1.1, 3.12, (98) Continuity: a.e. with respect to a lifting 34.8; - of linear maps on ~ 4.6 Convergence: a.e. (74); - at infinity (54); - in mean (76); in measure

18.14,28.15; - of a martingale 31A-D;

3lD, 31.11 locally in p-mean 31.2, 31.11;

Daniell: integration lA; - -, of linear maps llC Darboux property: 24.12 Dense: family of integrable sets (86), examples 8.8, 8.20, (165); - subsets of i€ 8.4 - !opology 34B, Cf. lifting; -, ~ in CooE(S(~)) 5.3;

pointwise

Density: 34.11, Cf. measure Derivative: ,locally integrable 22A-B; - -, existence for scalar measures

22.6, 22.7; - -, existence for almost weakly compact measures 37B -, scalarly locally integrable 37A Dini's theorem 4.12 Dirac measure 24B Direct: integral of Banach spaces 7.22; - sum property 16.10 - sum of Riesz spaces (20) Disintegration: of a measure 36A; - of a tight measure 36.3; - of a

support function 36.8; strong - (36.3), Cf. 36.6 Disjoint: elements of a Riesz space (19); - Banach-valued measures 3C (31), 3.17; characterization of - scalar measures 3.8, 6.6 Discrete (= atomic) measures (210) Distribution: 28.15 Dominated: functions and sets 4B; - integration lattices 4.4; - Baire functions and sets (66); - Borel functions and sets (92); - sets are precompact 5.4

344

Doob's martingale theorem 31.9 Dual: of Ll 21.6, 21.7, 31.7; - of LP 21.7, 37.1; - of a Riesz space (28)

Egoroff's theorem: 18.11 Elementary: integral lB (3); - -, associated with an elementary content

1.1, 3.12; --, *-continuous 3D (31); - measure space lB (3); - -, *-continuous (31) Equi-tight measures: 24.14 Equivalent: functions modulo negligible ones (78); - upper gauges 8.18, Cf. 13.8; - - have the same dense dominated families

14.4; - - have the same essential sup-norm 20.2; - - are simultaneously tight 24.16

Essenti~l: supremum norm 20A - ,-open kernel 34.11 - upper gauge l3A essentially equal upper S-norms 7.15 Expectation: 33A, Cf. conditional expectation Extended reals: 5A -Extension: of an elementary integral under an upper norm lA, lOA; - of an elementary content on a clan 1.1, 3.12, (98); - of linear maps llA, llC; - of the Riemann integral of step functions lA; - of a positive form on ffi+ to ~

Fatou's lemma: 8.11 Field: of measures and of upper gauges 25A-B, 26A-C, Cf. 36A-B; -, adequate 26A-B; -, integrable 25A; -, tame (230); -, of integrable variation (218); - of linear maps (224) Finite: sets and upper gauges l3A (138) Fubini's theorem: 25.3, Cf. 26.5, 27.4, 36.4 Full: clan (= o-ring) (66, 67); - integration domain 6B, Cf. 8.4, 6C, S-measure

span 6A - projective system or limit 30A

Gelfand: transform of functions 5D - ~auer transform of measures 5D, l7A-B, Cf. 10.7

Hahn's theorem: 6.6, Cf. 6.7, 6.17 ffolder's inequality: 12.3 Homogeneous (24) Homomorphism of Riesz spaces: (22)

Ideal: of a Riesz space (= solid subspace) (18); - of Loo 20B Image: of a map 28.17; of a measure 28A;

of a tight measure 28C; - under a morphism 28.18 - of a (tight) upper gauge (244), 28.11

345

Increasing: (24); - seminorm 4.7, Cf. 4.8, 5.9 Independent random variables 33C, 33.4 Inductive limit and system: of integration lattices (42) - of uniformities SA Inequalities of the mean: 20.1 Inner regular weak upper gauge 9.12 Integrable: fields of measures and upper gauges 25A; - functions and sets 7C, characterization 9B p-integrable functions 12.8 Integrability criteria: 19A Integral: Cf. elementary integral, integration -, Bochner 10A,-11C; - Daniell lOA, llC -, compactness properties lOB

of a field of measures and upper gauges 25A-C, Cf. 36.4 - of a function lA (2), lOA -, Pettis llA -, range 10.3-10.5

representation of linear maps 37.5, 37B, 38B -, Riemann lA (2), (36) - of a weakly compact linear map llC Integration: Cf. integral

of a disintegrat;d measure 36B; of a field 25A-C, 26A-B; of the image of a measure 28A-C; of a linear map llA, C;

- of a measure defined by a density 22B; - of a product measure 27B;

of an infinite product 32A-D; - of a vector measure of finite variation 9.1, 10A,C Integration: - domain lB (8);

lattice 1B (3); - -, generated by a family of functions 1.3; step functions over a clan 1.1;

lattice, countably generated 1.3, Cf. 3.16, 5.12, 13.9, 35.3 Ionescu-Tulcea: 35.1

Jessen's theorem: Joint distribution:

32.3 28.15

Ko1mogoroff's theorem: 30.6, Cf. 33A,B

Lattice: (14) Law of large numbers: 33.1 Least integrable majorant (143) Lebesgue's theorem: for weak upper gauges 8.3;

for upper gauges 8.12 Lifting: 34A-E, 35A-C, Cf. (305); existence theorem 35.2 - subordinate to a dense topology 34.9, Cf. 34.7, 34.14 strong - 34D, 35B; = - vs. strong iisintegration 36.6

346

-, of

Linear: (24); purely - (33) Localizable upper gauge: 2lC, Cf. ~trictly localizable Localization principle: 18.9 Locally: almost everywhere (loc. a.e.) (140); - integrable functions and derivatives 22A, 37B - majorizable 15.9; - negligible (140) - scalarly integrable functions and derivatives 37A Logarithmic convexity of M1!g: 20.10, 12.7 Lower semicontinuous Baire functions: 6.18 Lusin space: 24.8, 36.5

Maharam: 35.2 Martingale: 3lA-E - convergence in mean 3lB, 31.11; - - a.e. 31D, 31.11; - vs. projective limit (268) -, descending 3lE; maximal - theorems 3lC Maximal: function of a martingale (272); - ideals of Loo 20.6, 20.S Mean: (76), Cf. convergence Measurability: ,-Baire - 19.13: Borel - 19.14; Caratheodory - 190; - criteria 19B-C; -, scalar 19C; - with respect to clans of subsets 18.20; - with respect to (~,gM) 22.4 - with respect to an image 28B-C Measurable: class 18.12; field 26A; - function l8A; - set (169); - step function 18.10; Cf. 18B (limit theorems),

21A-B (norm- and order relations for measurable functions) Measure: Cf. elementary integral, content, extension

, atomic (= discrete) 24B; - bounded 13.12;- with base and density 6.7, 22C; -, complex 3.14; -, diffuse 24B; Dirac - 24B; -, equitight family 24.14; rr-bounded 13.13;

, induced on a subset l5C-D; -, positive lB (3), (27); Radon - lB (4), 4.11; - on a completely regular space 24.3 -, scalar, on a full integration domain 6C -, tight 24A-D -,semivariation of 4C; - variation of 3B-C,E - space, elementary lB (3) MinkowskiTs inequality: 12.4 Modulus: 3E (36), C f. (13) Monotone convergence theorem: for weak upper gauges 8.1; - for upper gauges 8.9; - implies the existence of an upper integral 14.5 Morphism of integration lattices: 28.18

Negligible: von Neumann:

functions and sets 7A; locally 35.2

(140)

Norm relations between measurable functions: 21A

347

Normal homomorphisms of Riesz spaces: (23), Cf. 21.5, 22.3 Norming subspace: (47), (108) Numerical = having values in the extended reals

Order: (12); - cone (12); - dual (28), Cf. 21.6; complete Riesz space (17), Cf. 8.13 continuous form on Loo 21.9 continuous norm 3E (36), Cf. 8.13, 9A relations between measurable functions 2lB

ordered vector space (12) Orthogonal (= disjoint): (19) Outer: gauge 9.11; - regular 9.12; - S-norm 7.23, 9.11 Oxtoby: 34.9

Partition: adequate (156); refinement of - (157), 16.2 Pettis integral llA Polish space: 24.7, 36.5 Positive: (24); - element of a Riesz space (12); - measure or integral (27) Positively homogeneous: (24) Pre-compact sets: (60); - are dominated 5.4, Cf. 5.7 Pre-density (308) Pre-measure 24.3 Probability: 33A-D; - space (294) Products of measures or elementary integrals: -, finite 27A-B; -, infinite 32A; *-continuity 27.3, 32.1 -, tightness 27.3; limit theorems for - 32C - and martingales 32C (288) Product: of integrable functions 7.11, 32.6; - of measurable functions 18.5 - of measurable maps 18.17 - of uniformities 18.17 Projective system and limit: of integration lattices 30A; - -, epimorphic

(260); - -, full (260) - of measures or elementary integrals 30B; - -, variation 30.4, 31.1 - vs. martingales (270) Projective sublimit: (258, 263) Prokhorov's theorems: 24.14, 30.8 Pro-measure: 30.5 Proper L-space 3E (36), Cf. 9A Purely linear or S-continuous (33), Cf. 17.3 p-integrable functions: l2B, 12.8 p-norms: l2A, -, standard essential (141)

Quotient: of a Riesz space by an ideal (22) - of ~p modulo M 7C (80)

Radon measure: lB(4), 4.11; -, variation of 4.18

Radonian spaces: 24D

semivariation and B-continuity of 4.11;

348

Radon-Nikodym theorems: for scalar measures 22.6, 22.7; - for Banach-valued measures 37A-C Random variable: (296); - independent 33C, 33.4; -, sequences of 33B Rearrangement: 28.15 Refinement of a partition (157), 16.2 Regular: Borel-measure 9.8; - upper gauge 19A Relatively compact sets: 5.4, Cf. 10.6, (37.7) Rickart's decomposition: l7B Riemann: integral lA (1); - -, B-continuity of 3.18; - content (4); - -, S-continuity of (34), Cf. 3D Riesz: decomposition lemma 2.14; - decomposition theorem 2.18 - representation theorems 11.15, 13.11 - space (= vector lattice) 2B; - -, complete (17) - Thorin convexity theorem 23B Ring of sets (= clan): lB

Scalarly: integrable (341); - locally integrable 37A (330), - measurable 19C, (306); - q-integrab1e 38A (341) Schwartz' tight measures: 24A-D Semivariation: 4C, Cf. 5.9, (104), 11A (116) Solid subspace (= ideal) of a Riesz space: (18) Souslin space: 24.8, Cf. 36.5 Spectrum: of a clan (53); - of an integration lattice 5D Standard: integral extension lOA (104); - essential upper integral, essential p-norm (140) - exhaustion argument 8.21 - upper integral (gauge) for a *-measure 9A,C Step function: over a clan 1.1; - are dense 6.3, 8.4; - on the line (1, 4); - measurable 18.10 Stochastic model: 33A (295), 33B (296) Stone: lattice (3); - space of an algebra 5.1; -Kakutani space of an upper gauge 20.12 Strassen's theorem: 36.8 Strictly localizable upper gauges: l6A-B; - are localizable 21.8 Strong: lifting 34D; - disintegration (322); - dense topology 34.10 - upper gauge 8B (87), cf. SUC Subadditive: (24) Sublattice: (18) Sub linear : (24) Submartingale: 31A, 31.3 SUC: 8B (87), Cf. 8.13, III §2 Super additive: (24) Support: of a B-measure or a B-continuous upper gauge (158), Cf. 16.7,

20.9, 34D S-continuous: elementary integral or measure 3D; -, weakly 4D (48), Cf. 11.13; -, Eurely (33) S-measure on a full integration domain: 6C

349

a-additive content: (34) a-algebra (= tribe): 6.12 a-bounded measures: 13.13 a-finite sets and upper gauges: l3A (13S) L-closure: 6.16

Tame: fields 25B; -maps (245) Thick sets: lSB Three lines theorem: 23.2 tight measures: 24A; -, characterization 24C -, products of 27.3; -, images of 2SC tight upper gauges: 24A,C; form a band 24.2 Topology: admissible (lOS); -, dense 34B; -, -, associated with a lifting 34.7, Cf. 34.9, 34.14,

-, -, strong 34.10 9(-topology S.11

vague 24.13 Tribe (= a-algebra): 6.12; - of measruable sets lS.12

UG SB (S7) Ultimately equal (291) Uniformity: generated by a family of functions SB;

of dominated pointwise convergence 24.11 of dominated uniform convergence 4B

- - on compact sets 24A of uniform convergence 4.lS

-, inductive limit of 4A 9(-uniformity SB Uniformly: absolutely continuous (120);

integrable lS.20 Universally B-measurable (2lS) Upper gauge: SB; -, essential l3A; -, extension under an lA, lOA -, fields of 25A-B; - inner regular 9.12;

, majorizing a linear map (104) , regular 19A; - smooth l4A;

-, strong SB (S7) , weak SA, Cf. HC

Upper norms and upper S-norms: 7A; -, convexity properties of l2A

Vague uniformity: 26A, 24.13 Variation: in a Riesz space (13); - of a Banach-valued measure 3C;

of an image of a measure 2S.4; of the integral 10.10, 10.12; of the integral of a field 2S.4; of a linear map (4S);

- of a measure defined by a density 22.3;

350

, preservation of 4.17, 3.12, 10.10, (62); of a projective limit 30.4, 31.1; of a scalar measure 3B; of a scalar S-measure on a full integration domain 6.5; of a scalar Radon measure 4.18 of a sublinear map (26)

R-variation 3E; - of U~ 4.14 Vector lattice (= Riesz space) 2B; -, complete (17); -, of measures 3.4 Vitali-Hahn-Saks theorem 11.7, 11.6

Weak upper gauge 8A Weakly: *-continuous 4D (48); - compact llC WUG 8A (83)

Zero-One Law: 32.4

*-continuity: 3D (31); -, weak 4D; - of a product 27.3, 32.1 - of an integral of a field 25.4 - is determined on a uniformly dense subspace 3.15; *-continuous: elementary integrals 3D, Cf. 9A; - measures 3D (31), Cf. 9A ~eakly - linear maps 4D, llA, llC

351

INDEX OF NOTATIONS

Sets are identified with their characteristic functions (5) • Concerning the symbol * see (32). Restriction of A to B: AlB.

AM (147) EP (253) 00

(256) Ecil

29.8 '\: A(p) (247) EX[MJ (75 )

AU (153) E I ,F' ,C' (47)

(i.E (fi) 19.14 El'F1,C1 (48)

(i.S (Y) 19.13 g? (65 )

93B

(fi) 19.14 ;:. (72)

93S ('Y) 19.13 FE(M),F(M) (78)

3'E (M) ,3' (M) (76) C (f) (178) f' • (74) ,g C (n), C (n,M) (330)

Coo (X) (4) gM,llgilM (199),15.9

Cb(X) (213) gm,gn (70), (197)

ff (fitE) (92) liglim"'~ 22.8

ff(fitS) (66)

ff(fit,M) (85 ) (h)E (111)

ce( ), ce (107) [h]E (120)

co( ),co (106) 1+ (g:, R), 10 (g:, R) (27)

DE [fit] (41) Io (g:) (28)

DT (302) 10 (g:;E) (30)

00 (303 ) Io (g:;E,R) (37)

DT

dm/dn (198) :te(fit) ,:te(g:) (41)

6 (51) KM (147)

o o· P' P

(239) K (158)

0 (210) f (fit) ,:l' (fit) ,:te* (fit) (64) x

352

lim ~

(40) -"(tR,M) (156)

lim (258,261,270) p (m) = pm, pM (244)

Lr =~(tR,M) (80) pU 28.17

4=4(tR,M) (78) pI (192)

£1 = £1 (tR,M) A

(78) :It: X ~X (54,57)

1 =q(tR,M) (136) 00 00

(185) tR (42)

~,LE _0"

4V (117) tR,tR (59)

£1 8.19 ~ (43,59,61) 0

tR@E (42) 2, 2, (198) £E (tR,M), Ii (tR,M)

£y(9I.,M) (165 ) 9I.[K] (42)

fit' 5.3, (58)

MfmA (151) tR (259) 00

M MD MT (210,212) ~ S ~ ~ (64,90) , , t,9I.t'9I.;:,9I.~ M (133) g(B,~~ (92) -p M (138) (9I.,M) (83)

M* 14A (tR,M) (138)

M* (fF) (32) i', (tR@E)S (66)

M* (fF;E) (33) 91./1 (22)

M*(fF;E,R) (37)

Mb (9I.;F) 13.12 S (56)

.«; (306) S (.91'), S (tR) (57)

mJ (2),7.16 S (f) (178)

(33),17B SUG (87)

ryS'~L m 17A

.s (IR) (1)

* (102), (95) .s (~) (5 )

m

m* m1< (141) a(G,V) (47)

, P

IIm*11 9.1 T(9I.,M) (173) m (261)

9T

(305 ) 00

NE (M),N(M) (78)

353

Ilull, lui (45) 1 (19,31) A

U (62) « (21,31,38),7.20,9.9

U1],Uv (49,116) i!> t~'h (32)

Ilull~' (116),11.8 II II (45 )

U(f) (165 ) 1 (48)

U «fn» (167) (47)

UG (87) ® ffii (285)

U(L) (233) [ f '" 01, [f > 0] (5)

U (50) (52) ~ :> , - (M) (74)

U (.8) (233) . , (f·) (74)

"If> (ffi), qf> (ffi), "ll'" (ffi) (64)

Jv (104,114)

"ll~ (ffi) 9.6 (117)

"llb(5O, (53) fB (82)

,.. 8.18 we (g) (335 ) (; ) (223,225 ) We(n,V) (330) SLdM (226) we (n,M, V) (330)

ffil x ffi2 (237) WUG (83) m

1 x m

2 (238-240)

A

X (54)

Xoo,Xo (57)

~ (158)

V,A (12)

V,A (14)

(56)

(54,56 )

x+ (13)

Ixl,lml (13,30,36)

[A} (18)

(A), (n), (x) (18)

(n)E (31)

354

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Lecture Notes in Mathematics ComPlthen,;vt l,aUet on ,equest

Vol . l" S' A. B. Allman and S. KI." "",n. Intn:xlu<;I,on 10 Grother>d '''''k Dual ,ty Theo<y. II, 1":2 pages. 1910. OM 18,-

Vol. 141: O. E. Dobb .. Ce<;;h Cohomolog,cal Dlmenslons for Com­mulabveRin'ils. VI. 176 ~tIS. I"70 OM 16.-Vol. ' 48: H. A.,neon, Elpaces d. POIsson des Groupe. lOClI~."1 Compacts- IX, 141 page • . 1910. OM 16.-

'101. 149: R. G. Swan and E. G. E •• ns. K-TheOfy of Finlle Groups and O'der .. IV, 231 pages. nno. OM 20,-

Vol . 1~: Hey". Dualolil lo .... lkompa~te' G, uppen. )UII, 372 ~'Ien . ,{l70. OM 20.-

Vol . 115 1; M. Oamazur. &1 A. Grothendieck. Schema$ en Groupe. I. (5G" 3) XV, 562 p~go s. 11170. OM 24,-

Vol . 152: M. o..mazu •• e\ A. G'Olh .. nd,...:k. ~hem ... en Groupes II, ISGA 3). IX, 654 pages. 1970. OM 24, -

Vol. 1153: M. Dem,zu,. el A. G'Olh,nd'eck, Schemu en Groupes III. (5G" 3). VIII . 529 pages. 1970. OM 24,-

Vol. 1504: A.. Lueo .... e l M. Be'lIt'" Varn'Ii!. Klihlenennes Compactes. VII, 83 paget, t\l70, OM 16,-

Vol. 155: Several Compkt. Vi"i~ktS I, Ma'Yland 1910. Ediled ~1 J. HO'Vlrh , IV , 21. pages. 1970. OM t8.-

Vol , H56. It H ..... horne. Ample SU~ya"et'e5 of Al ge~fa'c Var'el'e', XIV, 256 Plgel. uno. OM 20, -

Vol. 157. T. 10m O,eck, K. H Kamps unci O. Puppe. l-I omoTOpoelh&Ot •• . VI. 265 Se'len. 1\170. OM 20.-

Vol. 158 T. G O."om. f on"" Translal,on Pia"" .. IV. 112 page .. 11170 OM 16.-

Vol , 15\1: It Ansorge und R. Han. Kon~r\lent yon O.ilerenzenyer· lahran lur I,nea,. und n'chtloneare Anlangswenaulgaben. VIII, '.5 Se,len. 1970 OM 16, -

Vol . 160' L Suchnlon, eo...t •• but.ont 10 E.godlc Theory and Ptoba' brh1r. VII 271 Plges. 1910. OM 20.-

Vol. 161' J. Slashe!!. I-I 'SpaC<Js I.om a Homotopy Pornl 01 View. VI, \15 paget. 1970. OM 16,-

Vol. 162: Harrah ·Chandla and van Ol) k. HarmonIC Analys's on Reduc· II.' p 'adlc Group •. IV. 125 pages. 1\170 OM 16,-

Vol. 163. P. Clc!lrgne. Equations O,llfll" nt,,,II,,s a POInts S ,ngui1er& Reg ulr.rs. II I, 133 pages. 1\170. OM 16,-

VOl, 1604. J. P. Fe",,,r. SemIna", sur 1"5 A'Sebru Compl';tes. II. 69 pa' gtt. 1970. OM 16,-

Vol. 165 J M Cohen. Siable l-IomOlOpy. V. 194 pall" s, 11170. OM 16. ­

Vol. 166: A.. J. Sllbtrfll"', PGL, OVer Ihe p 'ad,cs: its RepresentatIons. Sph.,,"ca l Funcllon., Ind Fo..rr"r Analys l$. VII , 202 palles. 11110. OM 18,-

Vol. 187: Lavren t' "v. Romanov and Vaslliev, Mull id imens,onallMerse Proble ms lor Odlerenll al Equallons. V. 59 pages. 1910. OM 16,-

Vol . 168: F. p, ~IC' son, The SI .... n'od Algebra and ' IS Appl, cat,ons: A conterence 10 Celebrate N, E. Sleenrod', S""elh B;rU'day. VII, 317 page • . 11170. OM 22.-

Vol. 16\1: M. RIr,naud. Ann.,.u, Loca", I--lenselieR$. V, 129 pagel. 1970. OM 16.-

Vol. 170. L.ctutos In Mod", n Anll,.,. and Applreallons tiL Edlled by C. T Tum. VI , 213 ~es. 11170. OM 18.-

Vol. 17 1: Set'Valued MappIngs., Selecbons Ind TopologIcal Propert,es o t 2' . Edrted b, W. M. fle,achman. X. ItO palles. 11170. OM 18.-

Vol . 112' Y.·T. Siu and G. T.lutmann. Gap·Sheaves and Extens,on 01 Cotre<e<lI ""llytrc Substrea""s, V. 172 pages, 1911. OM 16.-Vol 173. J. N. Morduon and B. V,nograde. Struc ture 01 Arb'l.a.,. Purely Inseparable E,ten'lOn frald$. IV. 138 pages. 1970 DM 16,· Vol 174 B. Iv ... en, Lonaa, Dc!t" .... ,nants WIth Applrca"ons to the P ,ca,d Scl'reme 0' a FamOl, of ... Igeb.a,c Curves. VI . 611 pagu. 1970 OM 16.-Vol . 17!t· M. BreiDl. 0r1 TopologIes and Boundar,,,s In Pment,. ' Theory VI , 176 page. 1\171 OM 18,·

Vol 176. H. Popp, Fundamenlalllruppen algebra,scher Ma nnlgl'ltlg' ~e'ten . IV. l!ti SOI, tOl". 11170 OM 16,-

Vol. 1" :J. Llmbe k, 1m.ion Theo"e •. Add,t,vc Sem ant'c . and R,ng' 01 Ouo"e"I., VI. 11 4 pSlln. 1971 OM 16.-

Vol. 178: Th. Btacter und T. 10m Olec~. Kobord,smenlheorle . XVI , 191 Serlen. 1\170 OM 18.-

Vol. 17\1' S.ml~I"" Bou,O;\lo1 - Yol. 1968169. e.poses 317·363. IV 295 pages. I\I?! OM 22.-

Vol 160. Semon .. re Bourbaki - vol. 196\1/ 70. Exposel 364·381. IV. 3 10 f>a9f" 1\171. OM 22.-

Vol. lin, F. DeMeyer and E. Ing, aham. Separable Alg"b.as ove. Commr..T."ye R,n\ls. V, 1!l1 page l. 1971. OM 16.-

Vol. 182. L. O. Baumert. C)ocl.c O,U .. anco Sets. VI , 166 pa9es. 11111. OM 16.-

Vol. 183: AnalytIC T"-oryo! O,Ueronhll Equat,ons. Edlled by P. f . HSIeh and A W J S toddart VI. 225 pages 19?!. OM 20.-

Vol 184 Sympollum on Sev.,al Comple. V'flables. Park Crty, Ulah. 197o Eo,tttd by R. M. Brooks. V, 234 pilles. 1971. OM 20.-

Vol. 185: S ... "r.1 Compkt. Vallab le- II, Mary land 1970. Ed'led by J. Ho,vath. III . 287 page •. 1971. OM 2 4. -

Vol. 166: Recent Tr"nds In Graph Th"ory. Ed,led by M. Capob,ancol J. B. freeMn / M. Kro llk. 'II . 2111 P"9e$. 1911. OM 18.-

Vol . 181: H. S. Shaplfo, Toprcs in Appro"mation The"'Y' VII I, 275 pages. 1911. OM 22, -

Vol. 18t1: SympoSIum on Scman"~. 01 AI\lorithmlc LJn9"~ges. Ed'led by E. En ll,1" . VI. 372 pages. 11111 OM 26, -

Vol. 189 A. We,l, Orrlchiet Se"es and Automorp~,c Forms. V 1604 ~s. 1\171, OM 16.-

Vol , 190: Martln\l.Ie,. A Report on a Meutl"l1 at Oberwollach. May 11·23. 1910. Ed,Ied by H. 0"'0"" V, 7!1 p~ges_ 11111. OM 16,-

Vol. 1111 ' Sem,nSlfe (lot PtobaQllrtel V Edlled by P. A.. Meye •. IV, 372 pages. 19?! OM 26.

Vol. 192' Ptoceed,ngl o! L'verpool S"'9ul .. ,1085 - Symposoum I. Ed,Ted by C. T C , Wall. 'I. 3111 pages Ii?! OM 24.-

Vol 1113: Sympoarum on tl'Ml Theory 01 Numer,caI ""ar,..", Ed.red by J. U. Mo,,"s, VI. 152 pages. 1\111 . OM 16.-

Vol 1\1.: M. &trll,r. P. Gauduehon " E. Maze!. Le Spect,e d'una V .. ,~t' A,emlnnoenne. VII. 251 Plllel. 1971. OM 22,-

V .... 195 ReQO<ls 0/ the M'dwesl Calegory SemInar V. EdIted by J W G<aYlndS Mac Lane III. 255pages 1911 OM22,-

Vol. lQ6: H'SIIK" - Neuch.lrtel (Suiasej· AoOI 1\170. Ed ited by F. 5'11"". V, 156 pagCol. H~1 1 . OM 16.-

Vol. 191 Man,lolo& _ Amste,dam 11170. EdIted by N. H. KUlptr. V. 231 pag!!s. 1971 OM 20.-Vol 196 M Hc .. e. Analylle and Plullsubh.rmon.c funCllons;n Finlle and In/,nlle D,menS'OMI Spaces. VI . 90 pages. 1\171 . OM 16.-

Vol 1\19 Cr. . J. MOlloch,. On the Poi"Iw, sC Conv",g~nce 0' Fouri", S .",.s. VII. 87 pages. 1911 . OM 16.-

Vol. 200; U No", S.ng ... lar I"tegrals. VII , 212 pagel<. 1911 . OM 22. ­

Vol. 201 ' J H . • an L,nl . Coding Thjl().,. VII. 136 pages. 197 1. OM 16.­

Vol. 202: J. Benedeuo, Harmon,c An.lyslS on Totally O.sconnecled Set •. VIII . 261 pagos. 11111 OM 22, -

Vol. 203: O. I( ,.,ut_. Aigebra,c Spaces. VI. 261 pagel. ll1n . OM 22.-

Vol. 2004 . A ZY9mund. Inl09rale. SIt\9uloe,es. IV. 53 pages. 1971. OM 16.-

Vol. 205: S6m,"a". P ,,,,,, L,long (Analyw) An,," 1970. VI, 21 3 pages. '\171 , OM 20.-

Vol. 208: SympoSIum on DIMe.ent .. 1 EqultlonS "nd DynamIcal 51'1· lems. Edlled by O. C hlltrngworl il. XI. 113 pages. H~1 1 . OM 16,­

Vol. 207: L eernst ...... The Jacob, -f'erron Algorllhm - liS Theo'Y "nd ApplIcatIon. IV, 161 pages. 11171 . OM 16.-

Vol. 206. A.. Grothendlee~ and J. P. Mu rre. The Tam" f undamental Group of a Formal N ... ghbourhood of. 01~11O< WIth Nom>al CroSSIngS On iI Scheme. VIII, 133 pa\les. 11171. OM 18, -Vol. 209: Procee<!1I1gs 01 LIverpool Slngu!a"t,es Symposoum II. Ed,ted by C. T. C. Wall. V, 280 pages. 1971 . OM 22,-

Vol . 210 M. E..;hler, P'OfeetlveV'''elleS and Modul., Form .. III , 118 pall"s, 1\171. OM 18.-Vol. 211 Th6(lrolt des Ma,rold_ Ed,te pa' C. P. Bmler. III , 108 pa9'l l. HI7 1, OM HI,-

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