From 510fd211dab8df9958f1efee94cbd8e1efee80ae Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Petr=20Veli=C4=8Dka?= Date: Tue, 18 Feb 2025 06:30:09 +0100 Subject: [PATCH] formatovani --- nahodne-jevy.tex | 5 +++-- skripta.pdf | Bin 59265 -> 59332 bytes 2 files changed, 3 insertions(+), 2 deletions(-) diff --git a/nahodne-jevy.tex b/nahodne-jevy.tex index 6bec564..bf31279 100644 --- a/nahodne-jevy.tex +++ b/nahodne-jevy.tex @@ -17,7 +17,7 @@ Pro ilustraci uvedeme následující motivační příklad, kde podrobně popí \end{proof} \end{example} -Tato jednoduchá intuice však selže v případě nekonečné (nespočetné) množiny $\Omega$, neboť jak již čtenář jistě ví z přednášky základů teorie míry, na nespočetné množině neexistuje "rozumný" způsob, jak měřit množiny. Musíme proto pracovat pouze s jistou třídou podmnožin $\Omega$, které budeme říkat $\sigma$-algebra. +Tato jednoduchá intuice však selže v případě nekonečné (nespočetné) množiny $\Omega$, neboť jak již čtenář jistě ví z přednášky základů teorie míry, na nespočetné množině neexistuje ``rozumný" způsob, jak měřit množiny. Musíme proto pracovat pouze s jistou třídou podmnožin $\Omega$, které budeme říkat $\sigma$-algebra. \begin{definition} Nechť $\Omega \neq \emptyset$ je množina a $\mathcal{A} \subset 2^\Omega$ soubor jejích podmnožin. Této množině $\mathcal{A}$ říkáme $\sigma$-algebra, jestliže jsou splněny následující podmínky: @@ -80,4 +80,5 @@ Přímo z této definice již můžeme odvodit pár základních vlastností pra \end{proof} \end{theorem} -\hfill \textit{konec 1. přednášky (17.2.2025)} +\hfill \textit{konec 1. přednášky (17.2.2025)} \newpage + diff --git a/skripta.pdf b/skripta.pdf index 65141c7c81bf1f21b028ad2f8f5e393d4eb7dd4f..011a02bc76d6de46d9f1c76f85ae76079b79c9fe 100644 GIT binary patch delta 11880 zcmaiaLvW@Iv~sOB&-*|Niu-;K6~h zyIkfdUr(C9(}$%qHvNotRj7QPdQq{-EdQ~dU8?x?a_$7QN(Ji$Q#0AI(>I^LP&wR+ z@@CZ4%#6oxaMvGO`*h!{qW2d>YAzAnR6fe?mmEBIrYC#N;Muh<`M)_tnV}a18_zS5 zLc*L2cjy=Fq)SU0c2B6_59*%(ARW-r5QNtTF?-)(Yj&RFM9%i3SR3cKD}!(1BuLpl z1TclSM3Mj(rHodgOF7yig+Fh{;~J1EL&Pya)n&G?g2^UPxQ?rug+XUny7d~?x5;Ab zix#*{Ke@>4$ELJvaEH&xKHZdpsw1I|b>x=;;uPgBt1qZM4mo`$g9!83_!ep7hJ#0FmPAh@N-Xfv#5&bh z*?9SDm*pLB!`f4Hec8+M`sVJ{M|&N ztwc@(9_9V60d@Y&Sl2In&1)#R$;hYI;lFm)euY$sn@5QL+oKC#hcsf$LLz}QNuYUS zm(vL>m&00J2mXyR)g&1s8+i#Ui-YwhrtPgXN9OKsA|EEX{&wy7;-%DC1t14~@e__A zL~p@mes6?}@93}vKhmR9t06`3x*(^>($!eU09xK?ySrqwW7*2i!n!W4Bss0DG(umV zBT1ktCz5{mASRzYqbaa8$-sMTWL|DBO>Qd@wML1|YF?kmNuRE_~}3 zWL{lvh+o3}Wr4zUT_mSJ7;MSpI7fAv%7EdbPPx5NpRn$!OdsLC=KzUlAquMPTtFPN zqiT1iE`JH5kV|^r_@mj}hU&2Ip)20z4>VF6{&bRAe7@MqyOU^^evMV*lP2g=43-wK z^$fX5;?d|D?`{Xz0yMwEDW)Sk$>5c#HICjVh+KGiR&lUa!u7_-^lNV6hM{!W-wtjU zW8aYn_oI1@&AH3 zo@VW(FrdV>-r4Yye!5+>K%v5|5JYm(v~0I32n~N}IL0s>&*DA$lUN8#oJ($O=U-QqCyi ziA2x#11^<^Ouh8iOaUvB1Wc+mFczqYJ2_g2p$PX%NNu@mHER%K$VYY}H;Dd*9tGhK zgV8v997@S|bWGWqNE-|Ti-e3%c;vtW8!?`f=r${8*(SLG;Xm=3W9rr`UJcDCR}&Fw zCH=v1o}rC3#)$A#gv3DYr=(6@Hz`5~mqv9?Gl0kLtOQR`SWgyOt5a0Q7HVxfr|p8- zZ5elfU?{%YW3?2L=U{PhWG@IbKGh`|tH3~;cp z2?`>(y17`G*dutYHS54@V=O=Aqb7?;s1IxB*0as&R#xw6<~LV&Hrq6}1umx1WSb-j zlOlp+!pV)gq|`QQLd*1wg1~8PHG~U;)AF2E> zdd6~nuXF;AKc?YPTs?-p`19U>1B>V8yI*K*rAh`g@R~B8hw+^gEA2V=cU@ zR-%YTtVZ~XqG~>JYo@zn=4$F81_UU*um`-X2ihv<6VU`_I^vJN%&SpM98bS#?5H zyXe`K(SIdImMLPzV4+8G1L762e(r1RCG;y|)F^q_gVieXDNoF*@~-?`?wQByhH6^X z+IPe2=i4{R!?Z&ptnFSg;-@6^8eaUCYe58#69>Crs ztb<18;xXgtQsL*Rjeo9ADVsn3SboL&AU?i^mI?OlH|a;+_5R@aNR|tps1ad+bw^1< z=@B#^O8ll}rPY0Y2>h!3wzsPH zLmZ;Ahn|<*D4{mhmP60omlbpp;u+YogWX|2QCj$1-ag@{352E(X)LGx)Hp8T_*xuf zUnH#KRECXr$Q*;(C3ti^(F*Hi{Fd6gFNdC`1tjKQt#!H@(J3$@%h%p+OQq&BzC?@E zx<|v!|D^hry^RF&`R6nu!OfN8VTNLDN5i+{Oz`c@>H13787+$${e1LV-Mpe#`0JZXYiqcF8FMQt`&`p!)-{o1jw3`|>_IbmQFEQix1s!*M+oi*&e zC15vANl}!NeM6F>a8wNbo@f_X)80hT6yiX8eq?ZUB*wg?pk7uU8>vi7PEL>I?w*?J z&fc-}u_ACq*TjPF<9WY>KtS@AC2oaz8AMi}q@psEG!+J&*{-?v(Q#pKM1oVj1X@U{ z!0U+Z0+@S4xi6Pez%K;&`B46*qih7jx4sBm|EVNzLsoHu(G`B?m0<`wp2{*VZAC}n z1Rc#I(4A9;){5aP2HR%fNRkD_THSQI75i+iMJ-V-`O;f+h}BsLuSGt1+3n3sWu?9To~lg`V2ZsM{`NNX!xpu zZeGTuLn8@N3T`Izh>$cU5puNQB&O^C6hsw8wLJH8ReqFD^(|H-Q2#annsV)a~2Fqc_vl^+=3` z0@ttxQaPE6x z0F7C~Fb-bT)VB{pgi8>rTVL;HFVI>7pcZ5Qjp|r|;;CR%U0%RS({KUJLh?~wR>@9< zL`>hVvT$pe13~^M%#fMu$&aKz!X#;Y#GqBR-x>yhm=jRN?B4)XH)W!Tz#f0$6)e9B zgU|=jaw}N)HhUFeXnjvRB?%R1D6A-~E2pL7K;MJ|TR8oJ;f56Pp(rH1g`PD449F7B zk_3R5=sWEeyPjGFRjmK`NZ7;|mA$9(;JC!YIl__t-hK+bxwF%mi<7m-$F=mgnP4fn zm9CwHrG(YwbnXd;l}H^keXgO!!=KLm^J4X$XA~1OA@jna7fzL%{oh* z^}A3#Z7X|au%sLsbu@dpeL657MJKC6`pDX*p<-r3TV)!_meq9;y_UOxbrYN%q}VMc zz9q+{kk?jqKfAS*wu$}LcEjoh(}>raXFeTScHsmI8&a>e+gJHP+^gaNEx2uh+k)=M zsW&s9>hVj^94%2fIqVO5zcj0iLB4UP&lxMvzxM=WRf;r^fsr3c(6i`0b3GH2bd6p7gdbCxUP z$T`CcdzH8bUjCm9A4ym$k9^}cm2I>wzwN+yeZ{O&P2$|=5*CGrwi}`a6(D-AKaQin?~$;8QX&_3K+$3m z_dLi0QMXfLjoY$n!5_38EZtQF;Z^ZWDPyLKD%XTbM4ulEnYQdd8mzkR_vs&hZp~Dh zwS!b$B=6!Cw~2u10{a_YePkR9E0VL1arWW(^P+xXN~|tqZBabBp81RldFoaws*>Wr z<%mR>e_a1*fSCH)|L#F)6}X64x+sd0%l~bi&S1TpM`U(&g z@k(xlzJx9qb+S1i9~Y=Q##w7pi0d6IWW?!&b8Qm2;lWc=!fi8b5rf=0<&lRl0xMCe zgZs`%>=SOSZMBPDr@f05&tunmU&lND`50Rh6DIk$XdvMq6nBw#Kdo`Bf<zdE1_+7cd{-%t8u6>PRGg3UeZdJZu$Fr_KHI$d@6!)OJR>73=2vW_@cuAKV26?_#IMLJ;hB{91d{Q?cfM2=|q z&H)E8?%OY1eV)2c3OmmJLXL%I(=(dX2SyG|j&0 zv#ystasQuh>W9NakX+gZvw|fLzhl z$mv=Nn;2_OgqT*Ozk5t3%Q&o)yc@QHodkOo>XS-qr6@OItnac)@GJ~pj;Yzm%6{cW z=S+WL%;3$t+xt-VsCQm(t*nCQE(-m0J7YETJOQh*krg5)|3m+|7jh3%(ZG8QIDjpP zfaGsBT_`N0<4ZZ^?5KtZkH!6?q47%CfadXZOh@`puF1FPxSm#nsZQ@$lwOevazvI9 zta%WW8%l`nt~&a6hp?Dk7VhBb8AwaS%#ub>ie*<+B*%l~!OzGS*HLdx_6HX9Sl17(T#n1!Ra@yYp5PPU+gLW>Zd z;>K^BhKd`{rmVRcSYCOOi0pB1!sp(R{v&8e7ZEw09)WyLGP8Z4xCFN70bQ#sm8>h0>i1@7z@m8Or&ix=*+xM;{(yor--9ZzDikPsxDxt0PT> z-Xjf^xu?M%CFz$zQw8SDiD*Av4Qa99Ija+qcRb1Q1kT&p*};rqiftwpiC^p<5EGLA zJ~Tf&79?>bqwSZo;j=SX3}h2&^^USa7G*9GEJmpmSNU~T7t_}UO+YpcTYk3~N$ude ziU5C4eUH*IW+tTL#Wc*%kaDzNNxsa#Y}o4H|A)J(z8QeWYcZLaWv$kL1;$EZ{*$%! z)-h6>!6FKmNyVmShH%tl>aOuhOk#S3Ro4amMax0f4@BMZ7e zf+Fe06gxhTJC#v~kdCvM1@R*n>$1t0{#9MGgE>l8#re1C8+(X3`22N=ft(_eqp%ep zPH@q6M4#c0WvLZMxZW7KNgEwRFT#vDOqyCC3ulFc$=RP?o@`@0YBBCETtvy!8y5U> z>sAnw{15I))%W^A1-KLT0KXzLD5XE;!uL{eg6O!^7t@o%Cjyh8X8MFqGo{oj#||NYq`F z{ldrezJ1Nriclf+_Y8#3?O-b@>zs;nfCHo@UUXfMw1bOM7|Is`HLR8x5l z>ZB}2W%+CDfX%xjb9N7%(Aw?(y?ruywXDr0Sx%`m3EKWW|1u*ZaPQg6wPup{wXA!g zoQR2l4tr1FA5cah6l6Onute}3do0X)x1vX8-9S}U3k)kP4YBhYZpTeJ|78aoK8)=v zek0L%t|{|;8#ZmPwCm|?swu#gtJCJ3knnw zX=qE-o=g=?%@wfNUfzbC?DiQERQ`fFpGyq7i*VQl0Ut573b!I5l{>syM7Qgd_O$WC zA~=Kg2)EZYVkSTA=^%OdWM1gD;GQ;qU2_e;Upg&Q@B z^T)?427-oZ5#WhriP+Pm=*BR+mkLVe^t$Ij0=C#7L}6ai^Y~!;tbO0U3GQyxUF}a3 zx!lU;(M% zd`_CuVcGG4i`zM#7g<@MmzGvO`yUkvui(zM<9ce*nIqRUiY2d+tn;7W$af3hmX;t> z7tJoFF2mjl9~M!urs+s}`s`$P#8LNL#60>r<2`ALtxp&4k2bL>k0D&Cb+j|oEDNLj zfGhC~L)1$%Rw{^{uiymqmk0?_06xhERD_+Bj zt7~o#XdZBw;Tkwz*PF~;?w+J66i(i)9Tc+XlxOG~^WN`SuV7HDm(0RSw`KKridcmnv$1`|*%ro?qM_IV!y;Y>Av>-Hc@1 z;k-P12J%X?=$|$kqAy4BJI_k3Bm%lJ10@#_eWz!NYG}(C!gV2^>A9Yv9Ji}Qb+I9Y zrmCi;g^QRz5~J~!*YFKhe|}0}TeoW#F3Xjl&Nv2Fz18k8VCIlr5Y5LxRp1-T17!QG z!aP%Nh?^@M1<^!fKNvkw^ZoPAY1<88X{6rCaS)KOMfuL@N9!S6c{B4NOsya2TF>nq zmPy#;^a?Pb!$cQm`P369O*rCWXZGB}al%kW$ti0%`RLL8dJx^vBHl}7KK&s`q^`z- z?IlCd5+y^x2VMIMgry(0y1MSw0e{!zhFD}4kj46F^&)%;7M8^0NH;IGcL5mzT7qQ1 zQM}a)_9!rFHa(E}vQ-rd2BYy&`0Qn_>+=J@Mg=8S9xF@8(=u9smEEBH^>Kk6`h9Wb zr_)e;eQmU?shnx6ExRsJoc`Rxo;Ejh2fRx|L$!B8EJv;6K#9$B&nmSuaH&M-fL>&_ zLQxnBG3aFU163|ELT%OvDq(W}O<{@ar!VR2Ozt>Z(PPyJ&?35R@-}rNBp{E)_fO_& zcEFARrH)syGGvupuU7GK^y1JaKaP;-mV~$m^Req?y+a7p^EFrY_Q|V$%g0++)Y}MI z=_Ly*89RNJc~7Y(t@ zI%U-k;tydh#eiyhm97HKQ!`ZjZO7vtj#Hi39SLwkHg)wppw|8b%nAKz9uZ2l#VBg+ zd(Jn1hsEq7fkW|n8T?0tBJ^Z*<7C)S|TRKs?{7hsI;wGdbqG#JHYGqwyld%v|>LSYjX4VnZDgm2PCd*7R1th zU|SgDX1nWm80+54vLx!hpeH4n&2+qg0NC>QYJ<7Yir`%L3`)Unm zaJM3vCa!`_-%D(v?YK^=T&Xor;sQWK(BaVnJ3grC69sp)eS1n6PU`>x@t;`ol^Mq7 zCtenjc+N*7H}nsIisMC^(4_s5=Uv7_-dmk-1D1RNijGcPTB|EmLoEGS));?7a=XoI zLITfG-*+0t?5G z09ZJ*pI9X<9)1<3UpC|k)I<}oB+D$~-G zc|`j|x+ve0e;&PL5DLEpEd!3~fc}9EVxLh~-DZ>xd7o^?CI1&gE2<^S7H=jV?N!@! z0gdPELLwSVpK;eQBOC6u4D-Wtar!t^h@ouJ&+lq5RIx0K7&(2!@v5@gvFP`IOvwr& zBmnSFWhOH0EI0tZIWSYX4lOzC2qeB+AWQuX;R9=_{TmSGNq^6uQb$d}BfByw78p*Q z^Fx|^KB$a8BOj84fTO$pRA6G;9O z3d{`*?&1a%Bm>Sv3jQ9H^9^$#7lJ30;v3ob@-af5SlWpwT5(n4F8Eu0@85-zBqY*k6n|@R2;Vaqs|?pE^y~Pq*vxG??Q|# zmZ7ooE`EmJ9sv!F+4(rzm43i%H(iTaJyy);kPP=+4K+e)GA)iHDjPaGlqA zq&DR(Co27hXlYI)R#QJsYj7lnBNf^ad^FA4mwN4Bc)JC8qO(d$_X-uzT*0zgEF~6o z5XJFRo_OwevecY1ulG+REHE8qa`xyb7>}Ai#fI(eaMCyTG>fx#U&RExbMx$Og=O}j zb{os(6Potv+xPM!(5o`D>g#)}XurX&=1=#Ybzu1tFJqprHRo z`^CDIGlBB+;WfA=s&uGjj4Cn_>H6(+y1`@D0z+^6%%d{P&z+5{0UlGcm0|Ix&D!@V z)6SNoAj#@%P5#;M?(?s(YiP==`d_AvKU(P0nh|W81$ZV`3V_ zLMD3iF76#C?pe11nc#2skeez$s%Y`@6q?ov;uvI8WCjMVJ_0(s#I%T)>`#;;5Ov4c z&zf-4J&Ptx<)x6$i2f#Fgto2{+K^jl?>cWBk#V}2j*aMn3$CTt3PrntFzskGl@1FPfUTQ?iVfFg4MMg-^IIDBL1he?U zsKDwrt2;h{yYMc1v4-19k|_P$?}U_9xr@QM&o!@7@;;>$OaH{_UT_!`VF$`c?h&!0 z>N*!58{9+(H5~?IBS~ny?FmbUC98$<)e(Hw&6o21%N?Uv$bBMlC;s&O`(e^s3!Ir% zdG_w0CU?qv7*w{mmxDunFCLwFo_lB^Z^vFYAdTGzzVMFK?G#ZbzS)DzpTiqbDjW}` z(DdPL3lz#(brd2Ux8bzdcTN6$BC1%&cb9F!a#QEzx5mzkwWj#y&X|{TrM>7e=WrB%(;ub^BC@0=QrXv0 zmj7D`;Glhv(Kj+nO$=A{Z2F~$=g!`sfK=RwMYO-x@2hGse~wHn35(HnsXgDaB2dn! z6WC`CE{$)akGjKw8geJiQl7?!#tS1xm=He8c1+2DFFJ$K4E>fAthz?3$c8g)J*KRP zw2)jRwGNMQ@$J(zNGB9|*o&x&rOQmh@2|ZSa1~f7?TUqnvj*0=Crl!H6WOu%pZId& z+|dWyV@e_$oym5DoA?OS(Y;E23K@S#vZ$-AWqR7 z9%O!qoIv$<#_uuq9|(wKRnXxS=THlI4f(}SE+6md>W|?eAkYA zg;&Gm^q@lSCu`dCs#7CCyNKOqGc#LIo1Dk88wNG#K%J>ru;j`Y&Ia8NyWQ2%m&84& zv4Rx0RHp}1WgOihG3SKI{1~HLP6%kN$QMCNU{R4xh2D_4r1>YsM`R=Sb#5ha@n!wt zvM#)NaIkv?h+%Q5WOpk&j^u>EN1T0-(;x0oMS`u<`Ewf?oYjO24zV(M9=@ndURCtJ zrZ2y038=pw`QLEt`*0P;6&qcA>^Xfq+q-+kW)}Y3RbREiRloaIf5xEn5)tR7g)p?n*%>Qen$UL4DMKVGCW(uOc(A?P|XNx?zu7 z7PemV%&ckGPn}%*lfqX3N)Db8Stm)_{vKBL*Id=p@#7#TFIm-ag3ra%8??VQYJx^6 zNF@nIZZfa^H0f(Kr@yB?y%*0gP0L9lZ$aWuO^0$}F-3O#aqa!xXI;b=v`2PCleS`7 zb<8J<6b_rkAYyXZgha!MRPs=Fyjk{&4m~JWTPC=a~q01J*o_zX!!(;}JB!(|K{d!9(tsLq0-~($lW1-{m z^B~{y=4p8jSE}# z+jF(U`|RiIgjOrG_-;zA2Xd{86c5r~*59=Gl2|gQ(PjBDPVX0dv$7wm4H>*T8~Elr zRDgX;hC~Z@i=dt^tnWGw>{vjX##60fFnvsB^?}ka1lGe;XJ{SAek?hFFR{pR=#+u% z`+pqa_HpRR;68(yq={wJNi3!4wJW-Gs=suoqdh~!?EeR3U^=4pxD4LeD3adgM{TOo zxNXw+n&RjxDu(a>*_j?HqI%MdV(KAksd`0Oi%af;N5xHZ1^Km#M3qwN<T>TdhmO!c-N3u;8&bQZxc~JbO0aC=dloChYh75B)w#&8OR^qZ1M zP@=OP0_2Q{o@37Gx8kJJKUx5;>3?*R7KX?%U2mF4i_0o12g`?>w7rb)hb+urp39fV zMv|Koz0vfs`5UnCaXg-?Uc{I1diSAvH=%W|N=~K6HQcXG0Rdit?eS0Pul@Y3%>4-2 zxl%)ZNmBykL%;&X_~w0Nt*`k;C!X6q>l^fs@-B!KNcGKGtz+mt$(~flW8YWjfaGWN zSX&PvZ1Wk_L;)i(9uvOfG1Je+$ETegwjYQPizeRb-d(ZYa46-<)%Gj z?YN^hoU_?z#0~zZsmaE5eDBfFPRpB!ncnLrYO{C3QTB&46=SMt3n-fQ4e{?gv$m*+ z@ZJXgPJ%~G6_1v{fBQL~?|Ji9<@_N7yR!RQ_gVGV1n z4JXTB3&3={D2bhe@)9C>xJH`>mL?xLA)!A@Kez;#Q$BcUXzniy)D1vU)`E58yFMI% zYF)^Xf;?8+;Wk4YZ4V9kzN)mH-`cY6|3}|ZkO`h8O8}easqu!jB)?(eq>Q$;aI~6w!U9q-tOBZuP_#9rnMn z{xT(7V=l>+j70v25%dK_>w&2<#mve4xkRe<9Y_qFVT&H@7@?>*m(GHwtd?8JVBF7* zX@#xc+>W1aiBGFn;U|{+1PL}!`7H>mz^B1ifUL~iG3|+lJYQvkwWdNJr%4 zj_AN3K^^yd$J6HVf zMbJF&LI^O9cArtd)n2ZsF19AV0jh}&YW`o^COyO#<>Ij5M+ph+15aj>ACQ|$kr2y9dKbJGj@+qa55Qg6#*T5lQqGF+9C58}2kBWpM z=%QhjE2}5cGc^?!;IdyCn4isZb2%5v`+*^KVnn%q!ch8wV{m!ZeCPzUUp>ogrMOb*s@JU5Ko=k$0Vc?X{jOfnh;>l4CV0tp z2-eym&j^04*?B<@FK`6E<5orB^+R1i!Iq#P0w-+x0`y>I=tX775+`t*U3C3$UQifo zc?3)wM4S^=O`khA?C~!o-U1?@ol;$)_kYVsHI0fYkgXitJX7+o73E=j_kufP1#IdY*z;e<2)mSLK+2fbS)C$aK^5X+@mZ zwDp(AHXD}Wr>vDG_Wlh%#nnQZo~f%%K85mgHsY(1i%kuknnmLpx&mt7?Xfg>AKcC8 zFZ4F&x5^h0FAuASAMRTh3j-dtdcDT~0 XkxN3P=o}LxaItbAP*F)JNh16Y(=r7# delta 11820 zcmai)LvWxCu(e~`*2K0wv2EM7-q^M$PA0Z(+jcTZCYjjD{TBb?zpK0JMX$O}SDo|J z8J+_Vngg$wMF8}%xE_9UHy<>xNwqa#6_SuUiE=`ZZYwEGSI8Nw8@&tUz+bOIT2PKMCy5bEFv6xCi zU@zaQug2rhee=uK_?Re25u&ZkdqDei>evlr0{VPuqMmaHJZyK$Z_>FbL1|$)cfeSU z>XAyOAmIX{%#K&O2uek&TZq6}bJb5$0>hq?sT_@4x&ne=7(NoAMzx_a=lyTJnk8=5 zOsryF1^|ai7YVDGC`@u0+`4V*t$JQ5_Mlat&h(ofxapC%>Gl+O6$XWvx@lNUJk9$0 z;R~YP=!@ywu_w{S)kKSm&luywzlBGw&#v6y+dH!0HaGd;bp``Orn(4EXK^>M_*_F{ zV@WL(oQ;O!es?fF9vn6oF3R-Pi=KqXXvBiSuL6N*zo5!fDT~-jU~q8lVCfVb; z@^1I;5WvGTXv2NNT^oa+??`Jos`Hd&-Ul{r>gZrlm=2MI)4)KAxRyGt>?Jd%!n$}F zM;3mJMV1a|J-DZFbX6J2W+2wubHNo$MP2*Q3z-eBX`r zzyTt}>UgDBR`F^)Zy1s3ArD|qU09tV5n!JxiHKXZc_%~;N(vt7IPbAD6=;rHCkv0wx zt(VfkIcE9fMp7oY&+3dH73zm$t$sPu&!mr1=`_yU_s&1Z$^A79V12klhwws+;zXp( z=+z_D{Hi<|9rCBe%z7vtRddsj=#}5P`)mLDw79iZxYkIX8*?IMqYt|?4A3a=B-FFE zi!*RB1o$k?|*pQ(cP@^^&izphqBeCwf46086SCY zPB`w&5pkvjGjn;&>$OFQZt65ulG`*_N*@2&9V8N@q%<`az~IbL!~_FRNl}rrkQ5iF zYuF{``Z~BW51)Qj%bkVP0H9sj)CI2u3#GHZRxN;{=(@G0V*stLTTmd=TvSljA~tmf zaXK*t@N?>f$a|A{A5`l&7Na%<)@qq=4yCa=qXZg`Ts`o+-oN@6(-OLv^*G#K&ZqlK zD4!JW(=TgJeD!EWDl0{`7DhC2vwe9`BHRtp(313#$n_3{1+NGe0FdJM0h)f18Ir5} zWPgTBt2k7hr};a<&S7zStJOO!{Y8TgR#HjvyBWgwc7Nzn7cHu5&Uz)v(5Ft>p2TU5 zWPHouXhZHs4DUHaJM|d&15Sr>@zAYjF55$K*bFuQx$D0)hH5dXbKET<%>$R@k;_dU zTrk90sv}j~IrvWIz=G${aKxQ_4v7cKAE{A0UT553fM&bJn#iKF9?>h&Y&;-Mf3Ij8OXL8_% z{+@49JU9tzHZH=9*iavfC3zU7;Mck-@R{=s@;Xu+3TN)nB!t$71YTHbTFrZSYECqnfEqoL5JV9&=}2TZ6jm(o;(5>qdbfV+^uZ<3U0$p}IxXWAwX zLzJ>K-Uuffg9nFWxX)7DW+e`6(2XC;Ss?}&ZR9afgs4%5DwIINEI3I)A6X%RgumYfVTFzV0gL}p33z?Fr=Pj98 z;QbY(8chQf8sVeJteoce3kHm@p8tZkxJR=8p;zBiH(?u8o>};HZf^e>G zF6PGea9*1&+OS&aYn%Bf$s*!vqgr_lYzsPVv<{CtTb;U98kbNSbefz)WI@7MSeP)f z<1Wedk{&R8;Ek}?;+MUtx|c0APpuldw*J?K8I{{?UhUuCioy#TfB*VBI1aKMWaaYg zz3w{t_A!A?Z{VWCKwQ%S8nx=7uVIQgyxukRQa_$md9N7{BwU!lHM5IZ;!&Mcs2oxg z@&Cq-cEWjf@p>|e`AS5`A}5`jBcPWc9o8v)hP(A#@n(M~cu%;;9)R)4{R7Prqg-d-7wn=69N@@B??P-eLd;Tmr!aPs`wCjKID^f7-v?ARPch^4x>rm6s_ah$-M)VL{(P94? zBm`9>)J(jX!J-BndZZ;2LY%=bMP`+Hi9{wZl5-CiPoEK*VVcbel4JRyzEcxdLJ61A zM#v!u8Iibs-*R;YLzq3Rbl9$30D~f$C>lB{WF+HX+rKKtTSnhEhMTnw!;SCLKy&a# z{XBid+BGPkm&K`P%c#vhWE7zh@y*%kYQO7ea73>2ufGQJps3OTA#Fs@m|MIZeUCHz|rz;lpEwiZsJ#))Sjtw7#0N64;C2Fj^)j3_5? zzV~lop_R_b1M2T6;lie3+dzs3&id)@M#B|cvmPmuleiLN&~WIM6#v*7p9deJ(9i-- zjZ{1Uq^I4HF8McsIr9HdIcu~3$PEU+-U~)MMQkFUZ>RNRV@OE0e=LgZpAk8cr=_gL z(29{dPrwFmstFWabz!f{-CV<=p|hm@tg-!+=5lCh1zY`IS0i0_hYa{voR|X&E#-n1 zL^@HihHIVh?*ukz`3={1Uyl1Sr}f8%rMw7$7~3a;jio4oC9bKNjR|<#Bq`9)3nz1&2-gwXU{8B#u zL4CeL6F7AxdTyGYtJ(quF(x4c zx7E7!d%$Xemedh;f*;+$bO{EoQ8+Oa?X$BdTze#E#4u?$i^zHM5ScB{ma4nVN+axr zvlAd|vK@t!8c$aiApeOxZ?PR!F&)_*o%RX09ld18fD9)E*IQ#fxuCmQPpZc(-b8?)WmTEVLi9 zNN=zQA6=Jxf~O0E{~LTk$Nc*!2{eV_x3q+QV-gWMKO(sbKDbTJvfR4J{DKrP$lI_3 zC*$b*85&NKL1X$t_i98oT(~7jO>dDtfQpt%9gfc0TeB{{GbOT&HHw%IK~H6JaJgr( z0Xg4sGiR*vBD! zfJJLBBX{oa5%agNWh1NH{ek$;KXxapVT)<59A~87FBpN)lWQxWGXzR9!gMHc>kh^r zaUM{RnEEDzl9Ml;t9eFBA;lPat~-JfQef-qB8PBR{)J&~eu8~RGMtu46hT1L6GH7{ zxMK>jRlK63qYf#cFPtWveF6J-Qz*(1WZR+T&|Sh@=pfsiFuRvPnb->K&dpU8@~6{h zU7BX7i?Q7DnY2Nr-09)s%hzpUUEm8dcK(IkG5UW0n}L70$)&cma=8}xOjF9lT+Uo* zt!zh_1vLpLYb7pQRhZf7{q<2=_E&zA)k4$M)CX0(y96?;-=?VLP0b#xgMq7%q@24c zRw4$KGKx9uT4@n>!bThbdE{+Z)iAG}sxyjo-OSTAU+MaN)6dNTp4SO2)s5wt%j_Zj zp7c2*?_2XAeamrDQvIg;2h(+Zqypfd=5qu!<`j2@MxJDB+@uI@J zrPe7}@}}lf)H}X-ae5VowUI~Ai!cPQ?oMKi-O_0c&pv6Qwc;}k_8b{jRJ80H6r@7e zE^HDRK9p@SA_mvoe`X@!^ISb`NtbX|tU>Jp?_Tf7@0zgv=6?II!@e|p5>N3)_6_yNp((@^OCu37n)3yw9Ok50 z^k!5-btJh3=tvu2YUAn_DGf_V1~|z%f5fnzIm{2w*DlP?RW7T4P}jvD_ejr#9Al=n za>a^l9moUi7>whSyo+Bg-VibPWIsh9Fq^Toe&X=-Zlx9~khM`!QkKtGfD>X3z<(#% zG7P>h9ztXkswhjSc=&CQ#Nq=jWT&0(fYWml??Up^7Wou{UND!(*Cdp=h%;o z6@l>6G;1ue(3)t5FL!A?Z~AMWuF?b#T>bMZC)c)yb@8@i^r(6lgQ_t)Sy)0YQ z^-TuI2TcIkH6?g|Y8niPS4{wguEeQbi2b=ElqYuk=Z`c`>P)t|tZBh-+k)|Jf01p= z#4<$@_?0_sBdbHz=`#T-+rJ4#ncw)l$=u72w~nEWcKG-D+hAK3Hid0BGLZKmRJ{_# z`KhCe*ianK=dZ?}@1lE2h`s`C**W?%<%7Eb%$23^XLa{K-+sQ}Klu^G3bn$`Y!hbj zh4Xseaol~wW|Nka2o|ac8~Pt$`*61pYE3lqWAYbY)?T8m8>!MKLDMGTe4&~_;Lqo~ zq0bl!Vly#K`o#2S02Mt4lS5wDW(h_YCl%>KM{o)rlmD=O@Z4O7QA-W4P@Bp92@YmueYOD(r_l{I+V8Yb%;(HZR>UG)E^}>q=Yg(^S zT-v{?19x`C#rugM#@V!HMyXoG&}|_Xlg_jov$uNQkfDF zyn}Ci^*NiL`ieZ~*+bZsr!rpY?vCvMbglNyfctYK;Kt+1J5h7HSDazJ{7SFy8(<+7 z?CNw5*HCxEY#Qzjo*y+^5LFWyZhlB~;h~RU8K_LmD}$mlHz@7l0D-T0uwf^vkPJdKiXtJlc49df=>Mde?ekX8#A|X~Tn= zQPiNa&-KhukgFXG&p&1VP5}sK*21IlL2fL?3le zmNk&U06tko?!iRgsXFhyQ%N3t|NP7FCN9bt{HCxJ_!0rcvFyYNNrAcq`d^V6N%xlJlR?Ky+>!$esq~6n zu_J5pP`(j!qw*aYT^Ac+*hg@;)nZNWb_v1w+1dD6+tAdZcG6^C@3@=6g3?}Rb~l${ zvioi=zw~XN{o$7_`?Wq`x)~%Tj5D(colIK%50bC)$SkiQ^1M!0X(qnvbAMyy6m zz8kpXRBYCBKkpS>-blVS&w*g?{h*%5;sEN5Sd zN<4nI2EYwKb;X4BWZ`7EDQn!{NiXUAw~(x)R3EPlG}7)BJt&+xv5|0 zjD%Xg4Uj32`z3*pZvA)_b+EhWMXQ(^I1JT)Egv;j7WqTguU{uMR+-a-mb98hh z+9Ld+ng>P`&ZShnByw2o7~9k(r0|Bu3v}_z&z&lE*@TpN1)dB05WbizkqZSmuyNRx zOu4S?sM#0r{K`10Q15#Js-%HLLSSD47-wGyXVSge&aXh4%3Dq)`Y(U+0JfubThp_e z?6wsm)uHrtTfsXhzVn}Uk`6yseAL(&2HGhXBVe~MOq8mu zFoC6qYY281>Gp)1kHM4yxu3MQj+FR6WCqm>ods1L8AHI%J&s1_1ng%@e=!bFAYV6L z6AQFIf@}jML@owSg<>=ch_biR+Xuf{kIQDJ_6 zmg={0pM)KWncv?8TI)U@xe7r2Pmp&87S5v_~+I_UT7g#^5#5c=(Vj5)(y)mNWQ6BuU`WV~nc`tpQJ5H>_Glhq&sJus(3xa3 zb$9^hUFUPNo8CnYHWZ-ds#~vp@;(znGDAKZTvZ9DQB!s2*E||2(mVeX*ub6 zLrXOo`zKe8g93yCiy(@a2Q*)Yy(w(yP>dOp@mhZ|ZGS7XMTWxL)s=C zpI5Q4#%c=M^^6eA#gLSgj#j_?<-dtnTv?zyo9>{KnFLKoU=WyQ^B#}kZ277mir{rXGhAJ4)NS8WG2(g${B!~z4H&agG;7U(hDEmNm=OQL4HV3kpa8!t6pL7JJ% z1@Y>j6SsCSoEJCMj3s0&Ik9jly0td$==DECpj;h(WndBk2&t3> zm_sjPC34D6N5d`uvQ`#lebILS-#z;8@#^HuVPj+PW=g(2JpX(kqLlEDTc$BKQ92C4 z1D1?^H$T9lTPS2QV8NH4gP{ivQd9CjYOTI0qZ_xZTYj{Cl{p6WEB;N&P1 zZ4zVRY1P6j5U00rJgCJD+Zol!)?~-`3(wXdAvmUZ$JZifI8Ml^T^a#MIEa@%yhj-V zMuh1FkrYG$Gy#r;%dl!o>SwJxV!pH=;rQGMK%D5Dv5)af9Z^|u&O1Lp0`n9jNUp*7 zALI1l-I_Ii4&RR5kfh=tUu_XgkoxF=?(^8p+Mcf(pcXM1APMd9;pt&y&UD@%d61>w zln))2+qFp(NO$Gbs}I0@cGxDXR{HlQP;F6o^Wfq(ZM_%)Vs8Cw$&GAE1AO zVpE3Oc7V?<6(!W?M+Vmga6H3W_Y{80ufEYfvD*t2d{Q_f9sq~r(54&p+8~^#YDijMjeN)pFihSS_`r5 zj(_AABxw5*IzFGw1wc zEMYH%XVU#@3MYKV?IZUyyK8iofj0D@6`?Eh`sV7l(_d&k==#q&o~QpTaiS^Ef2P9-XXCM7t~Sn!|%^qcVK5hkz=^I}p! z1>|&Sa9koiyCek~v^uMC;(lHItoaLFw`$f|RwxJVgz}&T5g0rBL97T`77{r{)=Xhh zvl)UUv8^#=Y^oXT*m`t|KUlqN6k4Q8GDkf{H%;nko6;uepHZop9f~60`e3v z7bCDMXqSgNvU7}aGASx>XFX*KWwAuUZ4^{kg#%FDtRj9)<N{`*1?-81&HseGHWgd*a^-B5j>tw~F_7 zzeX?DUag(ATZ}bQv6JtBODQQO_E27-wr~RKmTd$YsVJ!09@#g+z%Ar(6w`6v%W0H?*ANO-@!ef@#pdh8 ztV4i-U)|lO$aC3x{Dg+w6E^gLSXVYRhD?#3--=k{i%q2E?F!n!Vbu>xlMzkDP`ElW z6q?>egkRloWD0(1VwqIb`Bv|$J!tr+>Bg+mzKSVe8x+9GZ|3b1@t;xTV|X%@+RK&X zba*mU+8ausiI5bcrI}VnXK-?pX*n^05JGdm!!7P}9nQrRm*%7LTMJJrlk`nZW3}h$ zBA9Ch+ilOqfW3K<&p2I@sMgI{*P_B5eky$4N*-*x_2k>CI&mH{vw4yUa-0$dId&@p zay$t}j0qrI8D6~7_(3$u0jEjH3~!VXVfCz#7pj@SvyBEIpEDt zWJ_$xWa}7BY&_iaGr&^2=U-z~jiY;yx_obEHvR?#T-9ZojY&-QvTT!9U5$5v%4HcQ z^0MrX+gFeeeT5w((6EWKg)wCVxuR2+GRrZQz6`8EeQSSn^QN*PlT@YI(YACFIipg3 zfR7I~T!A_vKDbs@l^)BFX|BO@YmBcvPUe*P^?S-RlzCU=ca-@G3ySuX`2@E8c4hJP zsE19UfkLiwU*Gjr@AGok*E3`*gByj5P9z{YjvM@Gp3ed?Fzt3r!rKg$00?ZH?WLcY z_W~*Otj&mSk|Xs+MqZrr4vy@#)N+)F$X)l(fA5gwy))Yi1qd0fC{^p0O!Ri+7-Lun zIV#*?Bo*qrXGWFKX@=l7oO2>t3ekV2vy2?DVV(|_1mrURPA;|F)o+mWc$R+FzPuea z!^LL9wMUX~IzLbdP}6(t)IE7dF~r?B=>amwH;6EIDhccfJmz8)H`)vyIo{zGij|#r z3O=7Nt{ZXe{rcXzJbm2-Uh+RZLpWXm{J3>g#?3z(Bcro7!LTzBZD1_?o;k6f_yE3h z?9rCVI^0)oHB47eC3>n5ZC&)oXFGRq70UQPdcF8OOJugZELDEOse&;qh@EGZ1JKt^ z>bQks_i-V4m?(yfgtj^>GcfBr_wj?0VTtGxD8l%N!7UFtSW0+>j1gPczwpuKB{iXI zGo~C)Na%TswRM zZFYS}lIx+R+cNpOhH+0Lo|B}_d2p&H5_HMiOl-yy(Mx95Kaps2!6wPIfPt77y@`LE zwkV#=&O$hz`SScYr+VV7hFh#H{Ef7`{2C$u0}`dzRzsP6gRhcnBS_u^SR#9BJ4wGS z3DgOykrIt189PEaHxXhX|Ji@fEBYF>3HDb?gvK7FJPZD_*-WY&%4TAr=x->jN4N*e z0JSKzX*ZGv&Ta$QsoPc(z_(Aks5dek#@k=ZJs*L_UsT&JcJcFvXdZ;~wF&K^l^zT? z%Hu3l8pNHNLaI2bb9i*Kx@r%LbQCx5h5WPAYFNZ|T1Dm+3D*EpyXw}w_65S;n8`I*3|33bsGlLHQ zU&au<5DytU&4TPYfU@~%*BmO40}G$3#+h>x)H4)}un-hqf@mx+`YI+pnC?ailmCadWG0q{7 z439cAfo1{G9(+fx1UC+k1T{&6-Jt;e7(H*2L>7dOl3(3=8>n$5T9S&)EWMezN2G zQog}r@ozUTSMokHr6iaV3cvh#)wZv^>6YBZGfbu*V<)^Ge5ZWo6$;THcCr%f_wUkt zaOfT7tm$(Ue5!Rao1cbK)^!_S9~NQS!iZ;_GjG3K&GRD;^0{f`=>CI^JLUPlljCeb z@(eu-#MGf|AWu2pM$3O&X}sV2nBeCjX&gy1c=&#bnv8pukcq`avul|=P0J@d%$;I9 z&GdZC{A=tErn@Vl2lH47L!%&EbL02T%eaXUXlATm;x8F-X|&V70=PRfX?_?a((5rM ziwh;wQ&PlaCyt!sY0HUXY5#zK;!X_f9lwv3)ieKx9tI4cASjwr{Le9Ilm5o^jpm5j)Ola6cvM zEyUC-Rs-@ zofEGjbj`mnC@LCpHe|jqDoIofI%-KSoE4lT;%uFxZ+Z;;X@!*uj`_ z43UtP!%O^c-pRW#?l_?Hi(9E`qd^bbEM# zdi54_@vaFh@;~c-OnMu~l@lcg2D}1=aprx^gf+pe6!HS&>X#55{~bg=$2Y=~3MhkA z)Ro+Yt{8jxIsQ^}WTj^h{9PQ8dYR?!_T^a%c-}vrYx3-~C(bJxA>&w9Opog*Ml4!} zWkRS>IuiGX%!H&}g89)S2KvM8MQ|Ee8gZm@PRbdEpC@MA98Z8Ak>~0wt&4jfamU<~ zD3J}=>cc<##wccGiV!#Or@Ozntf0QTymLr3O#gJr#QyHOe7a{UzCJM&$9z-V4GA61 z<)h(GcnYoY9%S$mUGJdcUUJpU_2U*2;_ugze4p|&&fmf|4xgDVHW8dSB}xKJE>KUd zy@%HXSg&^wI=yi}gE=a?!PdbscIMYkAy?!4==Nrx?~XpmZzyoqt^(-C^Giv5dqG?V zJ!VrT-YhTw4h&evx<7g2jy_>CTd;+0*mz;;LNSSU$~$Vkq}f^2C>%T%A>9;kLDc-H zXV+n&t-T9iA(CWN6pqi@QjP+`kGhzSiYB{?m0uZVWB>Vh;xAR*;ZurkzkaE3_mN9k+4ZdP{arfEs5|Kt8-q^uVb&+;+->k*eM!42m<=7EM}H@ZEBQ@o zjh)EuF~ZNo{p#lBhjDt0M*kVZC?3z0L+1xqaq-ec<)eX49)(=QwV zr1RhM&hWyO=C*E)`%mF(J;pGDXQ<*PJ4Z>&?&LFI$*UB0a%H!(BU>S>*N&2wx{_1t z)I+EAo(FnyCtrv`xFS1C+kfhp+*3Xfe41gKF6>T0;LgLnK9O>5z#JPy>Ud@0HIc} z_=)7z2xL1{mJ$-C5^UQ(nO;y;BIHIQct;|VcOvpyAqZR{9HR*8cAyD$kP3B3P9kW= z0VhNu-nD34rN+nie}x?gMgA5;fkJ;p{dv{zktOZ}Yne?*e2lM4%geGEi59@}ZNuN{ zKHn$flfbHJqhw$%KtgZ>!SCRv5_$=`~%Qiocl zU|(K+xG7lgQ?f%;g}k}bc!9gvcYi->jE2Sx?zqp;9Rf+H&g}`+$|UKZl6yu3$H~C~ LM?oR3C;|6BB~i>+