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fe ee vexily- Btn > Olin zoe OS m=O ie Peo eal a ae ee ee + fy : _ 230 bila f Since jt fs!) pune Wwe aloaga= fe partie. yp laiizo Dnt 0 GPP n=0 = __@ [sal = Zin day = sla wok ——— lov ta Cn, not — “Peool @ Tnangle inegualihs fox Sey Ate 1 : ante. Comsidey Io tebg ll = Lng ne > a = inl) 2y47 4c ny ENN = = Ios Zale aioe an Int £9 he fn yt they 1 i tel 2 ie a 2a -$—__, 4 ———— eee Bi Fines 2 Bn i 2 fae 2 te Megs | + ii ———. Se 2S an rn ea PE incquatiby is frug Axeaih 4 ‘| a ty ne doe of EIR Pee yj} —Schinarte dep uciti hy ie for ny ¢ (at 2.28) a_Uorn plex bilberk Space én y >| e tell Trgl for nucdt if wea ox yso then \ rs) Consider mn fo ry gO — po) LE f 2 Oe Indy Andy Weel i 4 kg, nol = C40 Tees ay > + Lely AY, a oe: = as | fE, ty Ln [fp Lg lh 4 | ig) Prove tne atove: L : Space = Ns Ay, Tn, ne) ge fy, ep tin) a ee EP EUs Wi but Boles fll) a nen ee fs aad 4) ee PS a \ i ay 1 Y > Zoli WEE Wien) a tail Say is a te 2Re dn yy Z [init pa lig ieee, oe iF : ar ve O4 2 2 pe iny> Zo pall Eeihe. yy 6 dle gl $= Fin pailicolax foro —ttaks Hills Spa _. Wit ; : 2 @ Moll: (of; 44;) 2 0 (Bg waning gies ef i park yeker oe Wig OTE. n= 0 abe al Weta fl? = B dln; + yi) wi it Bes (nj tg) Iz ev Zn & lol yl Se ence dee 0< Ing gyi 2 Whale 2 9d > PY dale Zney Wye ESS —# Tar ES mo BED Syis 34 ii (2a ime iar vip tt. aera iz ee a eee or KE Fat re Chasen wa er Sa 8 eer 2 ese Neh | Gonsidew 94] m=) ao 6 metus = of 3 i. 4 Hey =
lagen) tg ee | Lond = he Lory ff Tea ny? Hf ae hs ee a + }eth es a dees in ner produte Fislphul by Frehid in, Won Noles: a7e yy = 0 then _ a ee Ikan oe ih Iyil is biwatlg fue ee! inntr peadute Giver angle bebweens the é i . ; ____ eectous z : Plea Te yt 29 ten (i) gs eres eax _y = - ® hen ce mY > = 2 . 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Se a : ~ ate nae (I i Oo vw a _ Siang see att peas) a es i pe Zp = ody 6 ToL Pyact to aes p 4 We aid ity yc Meee ot eqhitra np) 7 = it ee ek p [Since 7 gf M -Consilar the ite 7 sh hfe hall nolo C = Fo bs conven of ay Qa es cloped = : 4 Oo ded not belems (PR ee) ea Comlece LO ts ore EM 2 yy Sf | g—thm: | TP OM so “prope x—cles ed linens SOO ah en 7 no ere eel I ete c= yen > fy OM oy Ce ee ei i. pa | nce 0) 3 true, teagan get _——— a | eatee dep yd = Zee den dye 2 Weg —— = fel* yl aoe rte reels ay Pee dey r S x fyi Pret = ign a me Ma ROSE Se > —— _ | flate: ze 1 4 | ar ooy ye oe —___— ¥ || DeRice 7, seg I dA za Fgh zd well uo) = Bac a [Neel 2 Wzo-yll =¢2.-y) Zo=y | I Shez.\* $ lyll = ys = zo | ar ee a diy WE th ee, eS SS SS, are arthogon | kal ¢ J || ret ee , fe) nig 4 chanie my ah eg _ i= Geek. ae SS ee j ere te ne Victosecd tneer subs pater ot tl in) meM 9 closed Convex aubsek of H J Min Hen MEN ot a Clot slindar Subspale | 4. ¥ gli Be er tocnes Jegib Aoi ( ae 7 a | ee Me me uch Pho _ El te firek MEN sénty nem we yen Go ———— ig I are -yall 2d lot me) P Goa Venti, 21) Verify 2 M+ Nop a swespare of HO ter Myint cleved ~~ __— msi Il | Let_d (Mn) ein =yoll=4 (Gora previous thn - 2 est 2a. «a | _ De fines » ZS meg ves aap h 4 Gay we Mie point st Mtn [trai fie Ai aR Wa ES n #8 a “eonvergeek ip a rauchy sep, = givea_60 Sao Sob a ee Kee ee 4 | te pnt a SS. ee ees ee Se | a ee (oa! wa SS a | Fe Te MEM po paper aed ecwbspace st ft — si Hen 3 HH Suc h thot zk oe i zB , | ees eree Lee 4 es NR Me Mt we | eyh above, in @ 1 beh nee) thy wy ela = Foal 2 hen Goal) BE A he 2 eee Take lieh’ _n na =o = =; =O ll ml: én ay =o |S ws sp ip 1D _ = Mie mt Vis fttin= reall 22.0. Zee Vee a /* | tan Cyd ave tauthy sep in Ws | brhonwmal set -- Wi 7m Ge Hesuce oe A sek O 2Geq2 cu 13 said be arinenp fait = ony “ Be Yn ie a i if Oe ae if; in) Wer = ir ni aoes clove = ne AF paeioe J. = eg ce MeN x SS mel fer Se) Wien | be a) Bile en eek io _t a Za Sbyle => ei i s Ay ey eS ten ep >t ie pies “=e -a+g 6 Mtn a pale fab. — | ae liseth oe 4 fs _§ bo ne 2a iy) We, vy Bejan | TP Ms _o cloted |.ntay* tubing te Ae ten ey __ —___—— fig TU me Peet Er z aie Moe He 4 ve Bh Cong i ley 34 Bp, Lt 4 eee 04 ine Alne ee ime rit a cloted —lintar Gubspace ct H revi os Thon) odin Bei LH 2 ee ibs ei? gti Vea PR is paras) dlement In ¢ in H - Suppos we _comite. i mo z Ll Se Ups ot [WS = Soll = |) 3° £m ee tell E @ define 1, - 3 én i> | now Were = 50 I =!) Biz Lr Zz eglh 2 F Thea repeating th e_pavot as in Chasm ___ | bee ae we get fy 3 We H (Se 3 rauhy | aa 5n (ERLE ape cA fe . 5 ta S also cauchy i] K=n+! = v La = 0 | Claim DT wez a Mang Font’ S Ey and) ay 2, apa SWod ie i et oe = 5 ae Ti(n)l| 2k en {zal >o- leaf fe Sire sues ae nlizedh j ee, ab n7 oo adie ie ibis sf par | Gren — Pee ee sa [Tall = ke|lnl) ¥ mae [ek Nt ee ene —— Gul ber Tule Tl gn Conversehy. 5: Suppote T 1 bounded i aaa (ayia ia To ‘pao sT( BD 1s Bounded! jh ea Eee 2) TZn wou nNzoll let ot be anu peink io closed voit splere 2 i Tees ABS fo Heak [lm iped (tals b av oe D for € =) u(t wy gives con bra ols chon tip? Tian )_does not tenay to Zero becavie (odtinucus UT Caaf > 2 ST vot torttinuaws ab Origia whch i Sinte Ts coo tinuous Suppse (to) iS ¢ segloPs wus My 2 OF Obs ned ot oT wes howe by can audity The @ TL9) = 0 ( [ep 7(a beg. bd seb co. Hameo wqveMl n. | eo st ence B+ Co. tia usual NS sign = Cl Weta Zk me pO) ; [ » Jo pe: T 3 bounded g @) aL fy nu!) a ae nN!) norm af Iineor Spare with I! I ee BLN nih er rl bac Page NS. i oe] | if SS ee a ee Sa ol BLN) il) Scatar Mulsplicap? + Je we aod Te Eo dhan yT i fnear and “hbeunded Nia ead eo at re x “Tetlemg Sup over inl ££ cS fe atl 2 sue iecDend fas i tales Ags = la) cup UT 2 lel toll Uae L ach Space’: Prot 0) dw’ are. Banach Spates ‘Ee # lls ond UTL=0 & Tmo Vaan fi lilies Urdecpoer = RE (h bilof rbesy > Since TIL is fhe supremum over non megukve L UTI) se fon we Ns “values tend => Til zo. | fr F BL (nN) bie. rovm’ cl de Bned at ap lt fm) ips! = Sip i Tia? GP jit Neg then ven wilh || nil St lt bM=o 4 | jr = I 240 ppt Tal eb By linearity and bounded mers _ Ca} I firsHy Jobs I (os haus BR ON NLD) at Dinca [px Spae “tnd Moron papers. = L Sine 0 Tiny on men so 7 se pec Ls a Wiitiiee Wen" t La) Aadikin Te 7) 6 BL(0.") toa I TT 6 Bigw nt) | fr au nen [NG 47. od |= bo Cool BG) in gle incgteabi hy | lek Ty Ty 6 21 ts nv 7. ee | Tok tng Supisvieen)ea— over, |Jnl ei | ST Cot + IG, G9) [ J iz {ll Tb My On aly J Taigio,g. Supremim over Nol 1 [ve Gee, Wt ol ST TI “i z [421 = Sup Il +T,) ty yrig t Se Sug Ut Col a ai 1 Cool ts 4 tp ell o *
