Matematika | Analízis » Mérték és integrálelmélet

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Év, oldalszám:2003, 46 oldal

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Feltöltve:2009. szeptember 25.

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u[Á퍦‚}Œ"‰sz"ˆŒ ž‡Œ «$¾)–‰ˆ ¤Ã ˆ ƒ"„ŸŒ  û     ð ð ŒsŒs   Œ"|™|}žuà ˆ ‡  ¾ o¼ Š«   ã 6‡"tŒsžvŽ‚}Œ"6vŽŒs7x"€"x{z  ð  ¼ Š«  «=披}¾  «ðó¼ Š   ¾   ¼  «$¾  ðLD<´7s(7­ˆ uŠ«    ¼Š «  ‚™Œ"6vŽŒsBètˆŒ ­!x{zi€Qzˆ u|}6‰s:~!}zi€<u7¡      ¼ p¾ziv O¯ƒ"„–i­<¡t£‚}‚i7sŸu7€<¦z´u!‰"}¹ €:([ z ÄÅ @ÅæÜ ÈÞ{ß/Èޙà`á2<ËÈ â"Åñã 7ƒ/~7ƒ"„"7s7sii¹ €O`‚ix"ƒ"„l"ˆŒ 6u!Œ"ˆŒ œ™Œ"z ŒsÌú 6vŽ$‚}Œ"6vŽŒs7x"€D‚}Œ"6vŽŒs7x"€wvÚ7­ˆ u7€ˆ "‚}Œ"6vŽŒs7Á+i¹ ƒ"ƒ"‡Qzˆ ´„<uD‰ˆ –Œs ¼½úê¾@ƒ"„–}­iu7¡ é 7ƒ"„pi¹

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‚i7ux·‚}Œ"6vŽŒs7x"€x{‰s7u}"ˆŒ ž„̈Œ u ¼ p¾@~ x{¹ 6¯¡ ” Ó7’ )8 Õ$Ó7וP #OÓ "Àzi7‡"7s7sii¹ €O¡2r   ã x{‰uv»ˆŒ ­t€<¦vyx{z}|}‚}Œu½~!i€Žz™zi7€·Œ›‰sŒ€Œ"‰!sz}Œ€ÀŒyÁ x›u7uˆ +7uˆ 7î ÄÅűËÈ + È ýÅ @ Ó —/´Ó7#  Ó¯—/D“22$ —Ó4#OÓ78 “’ Ô × "$ Ù  Ô  •› P ” Ó4’ 8+× Ó ’ " (  L # ’Ó    “ ‘ ¼ p¾L # Ó7’ 8*× ÓÔ ”›Ó ‘ Ó7×¢×æ”   : 7ƒ"„"z°ŠŸ Ï á Ð ÊOà2Í&Ë + }Ë â ` ŠÒð  J O Q ¨ Š J ‰ˆ ð  JO Q  ¨  ŠQ=  H   × !&’ 5 ¼ p¾ Ó7’ 8*×   #-Ó*”)#OÓ¯—“"× !1’ 5 8!Ó¯—{Ù$Ô “’ 8 $  5 Ó!’ —<Ó  Õ<“Ô ”Ž“ ‘Ù{ —/—5 Ó7’ #/ L #   “ ‘±“’ Ô ×¯“"Ô “ ¼ p¾& L “Ô —Ó78“ (  L # “  L ” Ó7’ 8)Õ$Ó7וy P Õ<“Ô ”y“ ‘ • " •

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• 8  ¾&/ ׯ•5 “ ’   “ ’ ¼      –ª   ׯ•5 “ ’  “ ’    F- “  †ð  ¾&/ Ó ’  ¼  !   ¼ p¾ÑÓ ’   –ª  ¼ p¾ “ ‘ L #   C3- “  H  “ E" " • 8  H   “ ’ Ô½Ô “#32 •’ 8 “  †ð  ¼ p¾ “ ®!‘ Ó78 $1#™× 5 Ó!’ — Ó  Ó4# $&#(× Ó¯—8 “’ ÖÔ Õ<“"× • ’    –ª H   ¼ p¾ “ ‘ L # -     !"$#&%()*+-,/.021  34 657 # $8 :9 <;";/ =<;";> 9@?BADC"C"C/EF  A-@ ” Ó7’ )8 Õ$Ó7וÀ P “ ‘ L # Ó ’   Ó¯—/{Ó4# ?-@ Ó¯—/{Ó4# Šw   H •8 , - “ Šw  Š -   û  “ E" " • 8   H       ¼ p¾ “ ‘Š L # ׯ•5 “ ’    “ ’ Õ<“  % *  –ª    ð  ¼ p¾ “ ‘ L # -  –ª   ¼ p¾ “ L E" "  #  “ •

8  2$ ‘E Ù# " ×Õ<“Ô ”Ž“ ‘ • "   êð  H   -  “  H   ¼ p¾ “ ‘ L # - . A" " • 8 H ” 4Ó ’ 8 Õ$Óו P -D. E" " • 8 (     H î  û ™ “Õ<•Ô    -@ Ó¯—/{Ó4# ŠŸ H  "E" “ pŠ+-    –ª   Ï á Ð ÊOà2Í&Ë + }Ë â  ³¡›£2žvŽ[Á)i¹ ƒ"ƒ"‡Qzˆ „"7€<­!&Œsf"ˆŒ 6¯Ã ˆ u}"ˆŒ ‰IŒ ¡6³7i¡ rtˆ 6 à ˆ u}"ˆŒ ‰y³¡`è-x{z´u½~!ŒšŒ"6Œèi~i"ˆŒ z†u ~‰"}¹ ¯¡ é 7€$6z´u!‰"i¹ €vŽx{‰u Œs7u¤Œst‰!7u7u7}Œ"vŽž€"x" ­  % Dvc7­ˆ ‚i7uxi¡ „<¦ž‡æ"ˆŒ znvc7­ˆ ‚i7ux7ƒ"„$‰s77­<·Á)}¹ ƒ"ƒ"‡Qzˆ „·Œ€<€"x"­&‰ˆ æº7‰ Œ€›Œ€€"x"­/ ‚}Œ ¼ ôð ´¾¤6‰¤Œs"¡2òtŒ "

$™Œ€€"x"­      ð ‰!iè þ ò Œ  / $æŒ€€"x"­¼ `¾ 7­!|}vÚzˆ „<ut‚}Œ"‰sz"ˆŒ ž‡Œ      êð  ݉ˆ š¼ `¾  ð ¼ ` ¾   $™Œ€<€"x"­D¼ `¾  ð     66¯¡-¼ ` ¾   êð    þ      w¼   ª    –ª  ¾  þ 66¢¡–¼ `  ¾ ð    þ   êð      ¡Øµ<¡ 7ä™z@à ˆ º7"ˆx u¬‰ˆ ŽŒsÀx"œ}œ±œ™žs7x{z„-à ˆ ux"uu    êð     " þ $pŒ€<€"x"­·¼ ` ¾ þ ð   ¡£Q€<€"x"­ " ¯­)Œ ð   êð  < % 3* +<% :2 ,  0 3-5)6  êð  ¼ ` ¾  :`7ƒ"„"zcvyx{‰u Ú  u7uþ !‰s$x{67ƒ"‰Ÿ vÚ7­ˆ ‚}7uxi¡›òtŒ / ‰ iè   øQ7sO7­ˆ !u›Œ ð   þ  êð  < % 3* +< %  2 ,  0

3-56     êð      @‚}Œè-|}žƒ  –ª / y‰7u‚™Œ"‰x{z}Ž ˆx v»{ˆx |}x{zÀ€-x"¹ ‡"7u€"7s6€(¡ µ<¡Q£2žvŽ}Á+i¹ ƒ"ƒ"‡Qzˆ ´„"7€<­!IŒs"ˆŒ ¦¯Ã ˆ u}"ˆŒ ‰Œ ¡6³7i¡ rtˆ 6 à ˆ u}"ˆŒ ‰2µ<¡èOx{zu½~!ŒwŒ"6Œè$~}"ˆŒ z&u ~‰"}¹ ¢¡ é 7ƒ"„pi¹ €yÁ½™x{‰!s´x"¹ ­ ‚ix"ƒ"„ O % ›vc7­ˆ ‚i7uxi¤‰ˆ ž7ƒ"„"z {¨·‰ˆ  çnx{ž„{Œ"zÀ7ƒ"„$‰s77­<šÁ+i¹ ƒ"ƒ"‡Qzˆ ´„"7€OOŒ"vŽž„"7€­ r ›û £Q€<€"x"­ Ž  û { ¨   çnû   ™<ux/‡ÌˆŒ œ}œ ˆŒ Œs  "¨        ç /çnû ™ª ¼ ¡6³ " ¾ $¾ |i7ä™z`à ˆ º7/+ˆx ~Œ‰ˆ ̌ ¡6³7i¡ rˆ 6¯Ã ˆ u}"ˆŒ

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ð J J ù  ¨  J Q ¨    ð J Q ¨  Ž¼ J t  ¾) J y¼ :ù   ¾    ¾  Ž¼ J  :ùw J ð J J" J Q ¨ K ðU³7ª7ª7ª ú®  /  J þp¨7 / $³7ª7ª7ªú »³ K ð   ‰ˆ Ú¼1¾Àð y¼1-¾ #›¼1-¾)¡Ý£Q€<€"x"­ Áíx{6„ux{zix{‰&‰ˆ  +7èˆ º7‰x{‰&Á)}¹ ƒ"ƒ"‡Qzˆ „"tvŽž‡"  H ¼ J J þp¨+¾ ¯­! J ±¼1-¾ð  J Q ¨ J ¡ 㠞‡" Œ J[è-x{z´ux"€€$ž‡Q7uˆ +7‡ˆ "øÁ½x{ž„<ux{zix{‰!Œ"zB|™O7­ z}º7"ˆŒ 6‚}Œu}Ž ˆx ¦‰w¼ Œs Œs v ¡ vÀ¡ À +7uˆ 7sž€f‰ˆ Á½x{ž„<ux{zix{‰)¾)}7sO7­ˆ !uŒ ¡Øµ"µ<¡ é 7uˆ 6utŒ"ž€Œ"6vŽŒs7‡Œy€Œè$~}€(i‚ix"ƒ"„   ›¼1-¾Q𛼠§$¾  ¼1-¾   @ª  ˆ

ƒ"„BŒs·³¡tè-x{z´u!‚ix"sD‚}Œ"‰x{z}/&ˆx v»{ˆx |ix{zêœ-ˆŒ u!‚}Œu}iˆx -‚ix"ƒ"„ €"x"­ ˆŒ ux{‰‡Ì"ˆŒ žux"s`"ˆŒ ‰-ˆ ¡r  è-x{z´u7­ˆ u6vc7œˆ -zšu!}|~!i€Oi‚ix"ƒ"„&€"x"­)ˆŒ ux{‰‡Ì"ˆŒ žux"s`"ˆŒ ‰-`ˆ ™|iI7€<€"x"­tŒs&x{¹ ‰!‰!s77ƒ-i¹ €š6‰¤Œs"¡ Á)}¹ ƒ"ƒ"‡Qzˆ „­"x{[Œµ<¡  ro€-x"¹ ‡"7u€"7s$xD7­!|}vÚzˆ „"7€ŽŒ­!­ Œ‡"x{z}Œu€"x"sz™Œ€(i‚ix"ƒ"„{Œ"zyu!™|~}€ŸŒs¤x"s$x¬"ˆŒ ¦¯Ã ˆ u}"ˆŒ ‰œ™Œ"zD‡$žs‰ƒQ"ˆŒ žu–uà ˆ è™}‰-ˆ $u!žžu½~‰ 6zu7ƒ"­™"ˆŒ žu7¡ UÁ+i¹ ƒ"ƒ"‡Qzˆ ´„"7€<­!w€$6‰s`"ˆŒ vBà ˆ

u!Œ"z}Œ tžvŽŒ"z}z  î % ™§ ï  ÄÅ`Å ÚËÈ +  È ýÅ @ Ó¯—/{Ó4#  § ï  ,- †î % ( ( ( •Ô /ׯ•#(• ’Ó  Ô6Ó¯—/{Ó4#  " •8+Ô “"’ ׯ•  5 “"’ Ô ×¯• 2 ‘ “ ’ Ù ’     •Ô /"ׯ•#(• % §™ ï L # Ó ’  2$ Ó78!Ó7#( $ “"’ ØÔ Õ<“{× • ’ ¼ §™ ï7¾L # - . E" " • 8 –¼1-¾    y¼1-¾2ð  –¼1-¾   ¼1¾ @ª      !"$#&%()*+-,/.021  34 657 # $8 :9 <;";/ =<;";> 9@?BADC"C"C/EF § ï  ;- †î % ( Ô Ó ’ I&(  • P  ( Ù{ —/—5     “Õ<•Ô@Ô6Ó¯—/´Ó7# y¼ t¾Qð  4Ó ’ #/·“ ‘§yð  –¼1-¾ Ž¼1-¾Qð     y¼ /¾ÑÓ ’ y¼ :ù ¨ / ù ù    / / ðÒïy‘ “ " “ 2 “ ’  & $ Ii•#™×¯• A" " “ Ô -D. E"

" • 8 –¼ J ¾ % y¼ J  ¾  JRQ  y¼ J t  ¾ ¯  ¾Qð y¼ ýùI¾ -    î % §( ï  Û ( ‘ “ " “ !‘ •# "æÓ7’ #™×  •Ô /ׯ•#(•  “# 2$ Ó78!Ó7#( $ “"’ ÔØÕ<“{× • ’ “ w ‘ §ð / )¨ /    / >?- 6Ô Ó¯—/´Ó7# o :ù ð ï! ‘ “ " “2 “ ’  $ I$• #™×¯• "E" “"Ô “ Ù{ —/—5 Ó7’ #/ ¼ J J þp¨)¾ $&#(× Ó78 5“Ô½ÔÖÙ$”Ž• " 8 “ 5Ó×¢×”›Ó¯— !‘ • 8 ! ’ × “ ’ –“"’ × E Ó*Ô • Ô E Ó  J B’Ó  žÔ Ó —/´Ó7# y  ¼ t¾–𠎼 /¾»Ó ’  y¼ :ù  – ¾ ð y¼ :ùn¾ - . "A" •8  ù  ¨   ù   –¼1¾ y¼1¾ð    –¼1-¾  J ¼1-¾   JRQ –¼ J ¾ % y¼ J  ¾ y¼ J t¾ ¯ª JRQ                 Ï á Ð ÊOà2Í&Ë + }Ë â ³¡r ¡Øµ ¡ é 7uˆ žœ–x{€-x"¹

‡"7u€"7s6€(Q‚ix"ƒ"„  H  ¼4¾IŒs% §™ ï žÂ z¡·¿–7ƒ"„p™¹ zi€†7ƒ"„u7u!‰!s$x{ž7ƒ"‰  ð ²/§cð  3/ @¨ /    / ™«¬ð ï ¶ œ-7x{‰s7u}"ˆŒ ‰™ˆŒ u % §( ï žÂ zi7€O¡†£€€"x"­yŒ6:@Œƒ"­ Œ"z}ƒ"*¯Áˆ žÀ€x"¹ s(7èˆ æ7­ˆ !u7€ˆ Ñu7uˆ  vŽ6Œuu+7uˆ 7sz}7€Àx{ž„{Œ"z  H ¼1    þp¨ ¾æ‰s`"ˆŒ vyx"€O(‚}x"ƒ"„  þp¨ ¾  y¼1  ¾Qð  ¼  ¾*¼1  þp¨    ¾) ! ð $³7ª7ª7ª ˜ °³ª ¼ 7ª7ª7ª 7«  ¨)¾)À‰ˆ ·u7€$6zu!‰i¹ €°Œs7s77€<‚}7s†Œc€x"¹ s7œ–}¹ 6‰xcè-x{z´ux"€$‚ix"s†u!Œ­!ux"s`N ˆx žv›Œ"z}z y¼1 :`7ƒ"„"z °ð <u!ž6u½~‰¯Áˆ ž€-x"¹ s7¯Ã ˆ ux·x{¹ ‰!‰s77ƒ"7u7¡æ£QsnŒw‰è-º7"ˆŒ

¦6‰!Œ"zy‡Ì"ˆŒ 6Œ"‰s7ux"uu tžvŽŒ"z}z $u!žžu½~‰¯Áˆ ž€-x"¹ s7¯Ã ˆ uxx{¹ ‰!‰!s77ƒ 6‰Ìu!Œ­!utŒs    –¼1-¾  y¼1-¾6zu7ƒ"­™"ˆŒ 6‚ix"s"}‚}Œ  ¼O   ´¾ð    $¡  ã "ˆŒ ‰­$‰ˆ s7ut7­!­!4Œsx{¹ ‰!‰s77ƒ"­! «  ¨   ¼  ¾ % Ž –  ¼1  þp¨ ¾ y¼1 Q  «  ¨   ¼  ¾  – Q ¾ ð ¼  ¾*¼1  þp¨    ¾) ŒsŒswvy7ƒ"7ƒ"„"7s6€·Œs –¼1¾  ¯¼1-¾Áíx{6„ux{zix{‰ÌÁ+i¹ ƒ"ƒ"‡Qzˆ ´„7ƒ"„ tžvŽŒ"z}zi¯Áˆ žI6zu7ƒ"­™"ˆŒ -€x"¹ s7¯Ã ˆ uxšx{¹ ‰!‰s77ƒø7‡ˆ "¢  Œ"vŽ€"x{z‡"7­!ƒ"z}‰‚}Œ     c‰ˆ ŒŽ‚™Œu}ˆŒ ­<7­ˆ !u7€ˆ "  –¼1¾  ¼1-¾ @¡

µ<¡rtsw6zu7ƒ"­™"ˆŒ u!Œ­ ux{v»"ˆŒ z´„<­ Œ›‡"x{z}Œu€"x"s`· ˆx Œ"|™|}žu!ž‡$žu}"ˆŒ ‰}ˆŒ uŒ"ž€Œ"6vŽŒs7‡Œ     é 7€<6zu!‰"i¹ €Œ À¨¼1¾Qð  –¼1-¾ ù  ¨ y¼1-¾2ð  JRQ %  J  J þp¨ p6zu7­!‡Œ"¦6}vyx"u7‰ˆ t|}7ä™z}"ˆŒ  ~!i€ŽŒ y¼ J ¾ Ž¼ J  ¾) šð J $  J(/ êû  J þp¨ ‰ˆ Ž÷"¼1¾Qð Á)i¹ ƒ"ƒ"‡Qzˆ „"7€"7u7¡¤£Q€<€"x"­y¼1¾Q𠐨/¼1-¾    Ž¼ J þp¨+¾ $    – ¼1-¾  Ž¼1-¾Qð    Žç"¼1-¾        – ¼1¾  y¼1¾)ª  ›ç¼1¾Qð  Ž¼ J þp¨ t  ¾)    ¾) J û êû  J þp¨* ð J þp¨7 J û  / J þp¨  Ž÷"¼1-¾)}7sO7­ˆ !u    – ¼1¾  ¨ ¼1¾   y¼ J    

   – ¼1-¾  Ž÷"¼1-¾)   ‚}6‰!s7z Žçæ€"x{z}‰u!Œ"z}‰7Oà ˆ ƒ"„ŸŒ4­™n ˆŒ ‡"x{z}Œu€"x"s`ˆx žvŽŒ"z™z <u!žžu½~‰ 6zu7ƒ"­™"ˆŒ $z<}66Œ$¡ :`7ƒ"„"z J ð  /    /  « ð J þp¨ 7ƒ"„êœ-7x{‰s7u}"ˆŒ ‰!Œ % J J þp¨ žÂ zi7€O &ð ¼ ª7ª7ª  «  ¨ ¾7ƒ"„u7u!‰s$x{ž7ƒ"‰Ÿ€-x"¹ s7œQ™¹ 6‰x·èOx{zu­!z}|™‰s77­¡ £Q€<€"x"­tŒ À¨:¯­ 4‡"x{z}Œu€"x"s`ˆx žvŽŒ"z™z <u!žžu½~‰¯Áˆ žI€-x"¹ s7 à ˆ uxêx{¹ ‰!‰s77ƒ    «  ¨   ¼  ¾ %  –  ¨/¼1  þp¨ ¾ Q  ¨/¼1  ¾ - ð –¼¾ % ¨/¼1@¨+¾  ¨/¼1 /¾ ¯ ª > ? ) /i   + 6O #{–1í+1õ+ 1í òŒ    

$(Œ€€"x"­t€Œè$~!i€O}‚ix"ƒ"„       – ¼1-¾  ¨/¼1-¾Qð –¼ J ¾*¼¨/¼ J    –¼ J ¾*¼y¼ J  ¾  ¾ À¨¼ J ¾ ð  y¼ J ¾ ¯ ª òŒ"‰x{z}{ˆx Œ"zšvŽ7ƒ{vŸiu!Œu!‚™Œu}iˆx O‚ix"ƒ"„   £QsO7­ˆ !u    –¼1-¾     – ¼1-¾  Ž÷"¼1-¾Qð –¼ J þp¨)¾*¼y¼ J þp¨7¾  y¼1-¾üð ð ð ù  ¨  JQ    y¼ J þp¨   ¾ ¯ ª    – ¼1¾  y¼1¾  ù  ¨  –¼ J ¾*¼y¼ J  ¾  Ž¼ J ¾  – ¼ J þp¨)¾¼y¼ J þp¨+¾ JQ  ù  –¼ J ¾ % y  ¼ J ¾  Ž  ¼ J t¾ ¯ª JRQ          y¼ J þp¨ t  ¾   ¡rts46zu7ƒ"­™"ˆŒ u!Œ­!ux{v°"ˆŒ z´„<­ Œy‡"x{z}Œu€"x"s` ˆx Œ"|}|}6u!ž‡<6u}"ˆŒ ‰}ˆŒ u›‰ˆ tŒsŽ³¡æ‰ˆ tµ<¡iu!}¦Œ

~|ix{z™‰}ˆŒ ƒ"x"€Œut‚}Œ"‰sz"ˆŒ ž‡Œ     Ž¼1-¾ –¼1-¾ ù  ¨  JRQ ð ù  ¨  JRQ  ð ð ÄÅ  Å c  ËÈ   Å ù  ¨  JRQ    – ¼1¾  y¼1¾      –¼1-¾  J ¼1¾    – ¼ J ¾ % y¼ J  ¾ y¼ J ¾  –¼ J þp¨)¾ % y¼ J þp¨+¾     –¼1¾  J ¼1-¾     ù – ¼ J ¾*¼y¼ J  ¾ y¼ J t¾¾)ª JRQ    :@7ƒ"„"zO î % $³(  –¼1-¾Qð   y¼ J þp¨ t  ¾ )  (́ y¼1¾ð $ ³  H % $³/¾) ðó³ª ¿–7ƒ"„pi¹ €ÑŒ % $³(t7ƒ"„Úu7u!‰s$x{ž7ƒ"‰ Úð  /    /  « ð ³Àœ-7x{‰s7u}"ˆŒ ‰™ˆŒ u±‰ˆ y7ƒ"„ cðö¼ 7ª7ª7ª/ «  ¨ ¾ €x"¹ s7œ–}¹ 6‰xyè-x{zu­!z}|}‰!s77­!u7¡Q£Q€<€"x"­ l‰ˆ ó|i7ä™z`à ˆ º7/+ˆx ~ŒŒ"6Œè$~}"ˆŒ z «  ¨ ¼

O D   ´¾Qð  –¼  ¾ % y¼1  þp¨ ¾  y¼1  ¾ -ð –¼ «  ¨ ¾)ª Q   ¬7€<€"x"­‚™Œ»x{ž„{Œ"z4‚}x"ƒ"„ «  ¨ ð ô ³wŒ€<€"x"­ ¼ O   ´¾cð $4‚}Œ»è-|}6ƒ «  ¨ 𠳁wŒ€<€"x"­ ¨ ¼ O D  {¾¤ð ³¡£Qs(7­ˆ !uIŒ –¼1¾ y¼1¾tŒ›€x"¹ s7¯Ã ˆ ux†x{¹ ‰!‰s77ƒ{zi7€ziv +7uˆ 7s6€BŒ&‚™Œu}ˆŒ ­<7­ˆ !u7€ˆ ""pŒsŒsyŒ  6vŽŒ"z}z <u!6žu½~‰ 6z´u7ƒ"­("ˆŒ ziv |i7ä™z™"ˆŒ 6‚}Œu}iˆx ¡   r €"x"­ ˆŒ ux{‰I‡Ì"ˆŒ žux"s`"ˆŒ ‰-® ˆ Á+i¹ ƒ"ƒ"‡Qzˆ ´„"7€†7ƒ"„›~66vys(‰ˆ 7uˆ wŒ"|~!Œ·Œ·€x"¹ ‡"7u€"7s$xBu<7uˆ ¢øŒ"vyž„"7uIœ™žs7x{z„-à ˆ u}"ˆŒ ‰ z捈 ž€p}¹

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