15
IT , jests , H ,V§ - µ #

IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

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Page 1: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

IT , jests ,

H ,V§ - µ #

Page 2: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

I : M E X → R min Icu ] = ?

uem

U

I '[ ufeo s.

Wta's .my

.in#IsIais=ftdauEfujybeHe.xf*uuYgimnsw&

:= Htdrlt of

D - a < x= inf I[u] ⇒ Fun ,I C un3→×

u€MQb✓H'n{un } ⇒

[email protected]'

.J#w

@ It ii ] £ limit I[ un ] - a

n

;

Page 3: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

un -> I ⇒ ffun → ffii

flails &limit f1\7un12g)

os { Hun . tlup = fHun12 -1117512 -

ztluir Hit

s.tbc.it#iSyutluFu=o.gqWMYluPuy.oN=oonar..skjwr

Feeder )I[u]=ftzltul2µt1ul#dx

I :Hks4→R i<P<n÷z

Page 4: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

- AT = AY I [ TTJ - SE KHP -

YEHL"

Tt ' 'dx → - a

un it%KI' \ Stitt - fat

Diss I

uxcx) = & ucxx ) €µ!( s ,

" of :#

soso.NET

. I

o Er,

Supp u EB,

C- I ⇒ Sapp U,

E Byx

tyua- fspsi

"

max,E¥YYua.ae?HI#Ya

*= { Eni'2nu*n:FdY÷mPYnind×

Ft

-2×+2> a Cpa ) ⇒ &<p÷

Page 5: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

t.pt#iiiywiI:r..n.÷÷Mx , ,=v }TFV

,uvll >r ,

IN ) £ 0

P={ r :C on ] → Ho : rcoro ,

A { C = inf max IC u )

ref VAKU

Fi,

ICI ]=c ⇐ j↳%%jItufo

Page 6: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

wins#sisKKristi , y€¥y ⇐ tee:X →R ,okx Aim

FUOEX, Qluo ) = Inf Qlu )

v. ÷

twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a

) : an Ea }Yxxxto

Ytu ) < limit Cmn ) o[ Tun-5in : y€↳Spn→x

Page 7: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

:# ,µk%q:H→R ,twv↳H Doc

aHE .tt#eb..w

Nhk . I ( coercive ) # +

µ :[ web.ws#Itq.bdfqiu ) Eliminf Clan ) £Tunw→IyTW

. IK .im#Isepica ) dw#t

linger

)=+-

- ÷Mt÷W>T ⇐ ,bµfu . ) ok 'T q(un1→*aF :$

¥eEu) g limihfqlunh - a K .

Page 8: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

/ s -1

.t.dk is you Ko Idris * I

of

Tokio W€ , Aw

: s -t.sk#EeW.D.IaHA;oko.Irs.6 , I

←HIT ) t.tt e ?

k . Nl Y%H a :c → R, t.us C [email protected]

Page 9: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

. ycnltlzacu ,u ) - < liu > ±Ian,v)|sChun . 11011 T.gl#pia:XxX → 112 .

|<bu>|E Chu " t±kIil:x→R .

:TMALL.mil#Yernigc= .es#e ⇐

.tt na. -

oetsi µ Qltutchtsu ) stqlwtcltlylvs ! ctsqil

^$

actututio ,ta +4 . au ) {t acuiytcittdluiu )

Each ,u ) + tu - t ) [ acu ,v ) tacit ,uD+( 1+12 acumen .

^

:u ,v ) tactful £ alum ) +a( v

,U )

De o<_d(u-v, UV )

Page 10: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

.FM#.&jwbQ.EuexgH.aiu.u ) $4/ J .t.INT owtanuytaiu ,u ) - ~

o1m;sY

* -1*51,61 Fisrxlk - R B-

Seth

.AT#oiHFc..s).xergub..yI-t.cFH'

' ) -

N ->F( xm )

fttosnfcu, - { Fcx .mx , )d× mis

Page 11: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

theory :H!→RoET/Fc×

.si/Ea1sTtboGs=1<-42*4

Hca)|{ faluftbdx < o ( 1¥r

neater ) E Lpcr ) |$p< It ¥2 ( N23)

?

? - '

t.dk#.~D:Eun-u⇒ Mtn] =lint [ un ]

⇒ ffcxiucxndx -4 F.( xmncx'ld×

rr

FCX , Unix ) ) → FCX ,ucx ) ) ae . in I

pw →k⇐

untfpu

I

Page 12: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

-/

. £%%E , .ws#T:E →F ( # .tw#

( Tmn )→Tu)[ bun- u d .↳H ) #

Jim Au - fix ,u) ¥61new , -f that - Fan 'd× {u=oof

Fcx ,us=f" fcassds

minYu % ⇒ ÷kµHow

HE !#÷£ty¥(A) Has ) Is alslrtb

o←<ytT

Page 13: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):

(B) zpA ,sth

. fg.pt# SP s.

4 #h→*

.es#xu.G:EIKE THA (B) , (A) HE #wIHf#K

s 's debt

t.IT 5TH= Id - T :'

#{ Then

,w > µ

.

= The ) ( w )

mikeEET

Page 14: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):
Page 15: IT jests - 213.233.161.92213.233.161.92/notes/course/VarMethod951/Var-2.pdf · wins#sisK Kristi, y€¥y ⇐ tee:X →R,okx Aim FUOEX, Qluo) = Inf Qlu) v. ÷ twsbtoItec.h1tIEHin@ncffaia3dwHD4w.etcanxy.waeRMIiW.Itepicy1-Slu.a):