archiviati - Rudi Mathematici
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archiviati - Rudi Mathematici
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• " ) " % ) # # "" % " ) • % • % " " ) 7 : " # ) # ) ) - 5 : 5 # ( 6 % - 6 ) ) # ## - - 7 − " % 8 − − − = ' = * # 87 = -* 5 : 9% # * % # :6 8 ) ) L # 2 # G 7 6 7 8 ' : 9 % # 8 ! ( 5 "" * # 5 # " 6 " 3 ≤ − ≥ − − ⇒ − ≥ − ≥ − + 6 # * ≥ − − ≥ − + + 2* ⇒ − − ≥ − ≥ ≤ − + − ≥ − + + :* ⇒ − ≥ − − ≤ 2 ) )) ) ) ) # 9 ) 4 E % # 8 " '' 6 ' 9 ) " ! # # 8\9 - " , % 8 3 + % - + # 8\9 % 9% 1 8 5 )) % 6 ) " 78 : E # ) ) ) - # " " \7 ) 8 9 * • " ) 58 96 5 " # ) ## 8 9 % 7 6 • ) ) " # - • 7 # 8\9 5 6 " # " ) 5 % 6 • ) • ) • " R ) ( % # " # # , ) - # 8 ) ) 8 9 # # " 58 96 # 8 L # : 5 K $ K 6 L 5 $5 O76K 6 5 K $ 6 Q A 2 # M ( ( # +# # 5 2 * :6 & " 6 6* " # 2 : " 2$ % " " 5% 5 ( " :& / ! 5 * ,: 9 6 # S " " % ( Q5 9 ) # . ";* ;<, , 5 8 , 8 # K O7 K 5 6 9 # 6 # K O7 7 9# 7= 8O7 8O7 87 , 8 # 5 <8O 6K , 8 # , 8 8O7 # 7 5 <86K 58O 8 # 2* :* , 5 : 7 K 58O K O7 9 # 6 5 <8O76K 9# 8 K K 9# 58O 6 5 <8 76K 58O 8O7 6 6 K O7 K 7 9# 5 O 6K 5 76K 8O7 8 ;< , # 8 * ( # # ) - 9 % 2* :* / , 8 # 5 O76K 7 ( , 8 # 7 ( # , 8 # 5 O 6K 5 76K ( , 8 # 7 ( # , 8 # 5 O 6K 5 76K ( # 5 76K 5 76K ( # 9 9 # 9 9 # " 9 # # ) # " " 8 # # 9 # # 9 * - ) " 2* :* 8 5 : ;< 5 $: ;<$ 5 5 5 O 6K K 7 K O7 7 K O7 5 76K 5 O76K 7 5 O 6K 7 K O7 7 5 O 6K K K O7 7 5 O 6K -: ;<- 5 O 6K 5 76K 7 5 O76K 7 : ) ) = + = ( = = + + ( + + + + ( + + + + + + + 5 76K K O7 K 5 76K 5 76K 5 76K 5 O 6K 7 K 7 K 7 + + ( + + ) ) + + + ( 7 =>) " \ % -?@ 26 + 5 O 6K 5 O76K * 6 5 O76K K 7 5 O76K 5 O 6K 5 76K " V ( K 5 76K 5 O 6K ' 7 K (: ;<( 5 = 5 O76K + ( + + 7< ( # ] - 5 7 5 # - ( ^ * - = + + /" + + + - ## =>) # # % )) ( % ) # + &) " " # 9 - )) 7 *8 7 27* 8 7 7 7 7 C C 8 = < 7 77 7 7 7 7C 7 78 7= 7< C C 8 = < 7 77 7 7 7 7C 7 78 7= 7< C C C C C 8 8 = = < < 7 7 77 8 8 = = < < 7 8 8 8 = ' 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 C C C C C C C C 8 8 = = < < 7 8 8 8 = 8 # ) % "' ) ∑ # " = % =∑ −∑ = + − − = = =∑ −∑ − = = L = ( +( + − " ( +( C C C C C C 8 8 8 = 8 C C 8 8 = = < < = ∑ # = − 7 27 ! # . # - 7 7 " 5 ) ) 7 7 7 + 9# 8 : *8 7 C # - = - :7* 8 \7 5 ∑ 8 # J 2 *8 # = - # 7* 8 ∑ ) % " 3 # " 4 1 5 #6 # % 8 " 7 -* )) ## # " :76 " " ∑ ∑ = 1 = ) ) = 1 - ∑ ∑ = = = = − + − − ) ) 3 − − ( = ∑ = − ( +" − ( ( -* 4 + 4 4 * : * 7 5 76K + −( + + + −( * − − + 5 ( + −( )) − − − − ( 6 5 )) + − + ( − − + ( 2 = :7 -* − − − + − ( -* 7 −" ( − ( + + K 7 5 ( ( - ( "" −( 6 = + 8 ( ( = ( − " 5 ( : ( +) + ! 8 7 ( ∑∑ − =_ 4 + 4 7 ( - − ( * : +) + − 6 : ) ) +( 8 -* = + + - ) ) + ( 4 − − # 8 # 1 + ( ) ' 1 − -* − − + + + ( 27 ∑ ∑= − ( = = − + - ( 5 − C6 )) )) − 6 + − − + +− ∑ ∑= =+ + ∑ = + = − − : ( : * 4 4 + 4 4 4 + 4 + (−( =_ 27 " * + −" + ( 5 ( + ( : * + −" +( ( 5 ( ( : (−( )) * + (−( + 6 )) −" +( − + ( 5 ( 6 ( : * + (−( + −" + ( 7 + − ( C6 )) 5 )) 6 1 ) ) = - ∑∑ = = + 2 ' − -* − − + − + − − + − ( " L # % " ( / " 5 − − = : ) ) > = = 1 * # ;<, ( +( − - ( ( ( −( - ( − (" = = − % = # ? ,: = - + - = ( ) ) + - - - ) ) ( −( " − (" + ( ( ( ( −) +" (" ( - # * 5 : = ( −" = ( = ( − + − ) + − ) = 5 - = ( = ( ) ) + - + = ( − - ( - − = 5 ( = ( = ( = − ( + - −- −" + ) ( ( ( −( − = - - ( + = - ( + ( − +( ( = ( = ( = − ) ( ) ) - - + - + ) (" (: +( − ( + (" ( −( +( − (" ( - ( # ( ( −( " 7* + ( −" − ) ) − ) + ( − + −- ( (" + " − " (" ( - # * ( % = ( ;<$ 1 ( = +" ) ) (" $: − " ( % ( = ( - 1 −( ( ) ) + − − (( - - ( ( ;< − - = ( − +( = + ) − (" : + ( % ( = ( - 1 5 ;< ( −( − ( ( − −) − (" + (" ) ) - ;<( = ( −( " # − ( * + ( + - ( ( − - − " - ( +( ( = ( = ( − + (" − - − ) % = 5 ( +( ( − = ( ( − - −( − = ( - − + () - - + - + (" = ( ) ) − = ( # ) ) ( −( − +( ( ( ( −" +( + (" − ( +( (" ( - − # C* ' ) ) # ) ) # - - # # \7 " ' 6 J − (" = = = ( = C 4 # )) % T 3 " ( ( ( − ' = L " ) " + - − − ' + - + (" ( (" ( (" + - −+ - + ) ( % ) )) & * ( G ' )) −- ( −( −" +(" ( - = ( − (( − (" ) ) +( + % = + ( - 1 - - ( ;<- ) ( = ( + - − " −" = +- ) ) (" -: = ( - 1 = # # " : = = , − ( + - − " − ( + - + ( (" \ ) ) , # " 77K7= 5 7 7P6 " # ) ( ( (" # ) ) ) + C 7CP , # TTT - 57 # 1 ' D +,; / ( 4 ' 2 % ) )) & ) ) - ) # ) * , *5 % % ! " * 5 64 ) # E W ) " 3 )) ) # # $ % # T # # * $ 9 - ) ) ) - ! # # ) S W # E# " 1 1 5 ) " ) 6 ) ) " - " % # # − − " 8 % % " " " < 6 # " + 6 > 6 " " # # 8 ) ) W 8 " W " " ( )= ) ) " 6 4! 8" " 6 9 % ! " 5 "" < 6 " 5W 1 ' " 1 5 " " " / # " " 8 # 586 # C 7K % - )= ∫ < 6 ( = 6 6 ) " ! # " " " " ) M # ) ) - , + # # # " ) " 8 " " " W 9 " % 9 @ 8$ # " W @ 8* ( ) ) )= 7 − - % ( )= ∫ + 6 7 < 6 ) ) : % " " # ) ) )) + / G 8 9 6 = − 8 " 8 − 7K / 9 7K )= ∫ 6 ) ) = − E / % ≡ + ) ) 7K $ ) ) - 7 "" + / ≡ + ( 9`7K ∫ = − - < 6 7 < 6 ( 8 > 6 7K )= ∫ ) ) - = 6 , !% ) ) - % = % # )) 7 ( < 6 7 < 6 7 + ( : "" 4 % ) < 6 7 < 6 ) ( > 6 + ) ) ) ) # " ) ) " )= > 6 )= & ) " # " % # G # ) ) " " ( # ! :A 7 B C %%% ! "; " / ( 1 # - 5 6 ( $ +,; / ($ 2 , ) " ( = "" % 2 ( "" # " 3 > 52 " % = 6 5 ( E6 :( * # # " . , 5 ) " * 6 " # " L *? G * % ) 1 9 % ) * # " D 4 E;6 : 5 * W # a) b b c ) 5 # - . " " % # # ) % W " ) " " "" " 7 # 2 J " ) " " # W # ' 1 3 % " # * # , # ## N6 = " # * 7 # > ? ( # * • 1 " " " S • 7 d @ 2 # " # # @ 1 * " % # ( 2$ • • B • = = = = " * "" ) \7 \ "" 5 6 A • ∆ % * 8 ∆ " " = 8 = 8 = = : 8 = − ( # " # % 9 H : # " # & 5 6 1 K # H 2 # E ) ) " * ) - W % ) " # # 5 6 " 5 %%% ! ) ";6 ' D % D ) : # * : H # H H H " E H H # )) " H H # H H H & H H % * ) # ($ ) − ) " 1 ( = 8 − # A" = " : # ) % - H A:T ) # # - T C )) # 1 # 2 D 1 3 " 5 ) 6 G " 2 " ( = : % # # 2 ) * 5 6 7K7 L # # # ^ ) # 5 # ) ) 7C # # 5 # A - 8C C6 # # # # )) * % * L # # # # " # # " # N # ) "" % # % ) " F = # , ## 6 * ) " " " , + = # % # # $ " , % ) ) ! ) ) # # 9= / " > + ? 3 ⋅ + ⋅ ⋅ = " " " " " # ) ) - - 4 7 # 7 ) # ) ) - 7 ) ) _ ) ) J # % - % ) =P * ,(( ) ) 5 "" > - ; # !N " ?6 % C ; " + % ) ) " )) - = " ⋅ 9 9 ≅ 7 )- * " ( # d # C # 7 ; , E* ≅ 7 " C 9 9 = ( 9) ; 7 7N 2 # 1 # - # " 5 6 " ! ) " , ! ) " N, ! % ) ) " 7 % " # " " % ( # 3 * ) - # ) , # ; % " " E* ; " 3 9= " = ⋅ 9= = " ) ( - = - % " ⋅ - = - ( ) ) ) ) - ( 99= 9 ( = - ) " ; U * & " " % : N & & # 5 # L( # - = 7" # ) ) = = # + ; # ) ⋅ , ; G + + = 7- () # ( ) ) N " & ) ) _6 , ' # # # " " # ; & # < , )) " " " # 5 # (7 " 1 ( (7 _6 2 " " 7 ## 1 3 " ( % * # ) # > E ? > % " "" / " )) "" " " # ## 8 58NTNT E 8 " C " 5 / " " 5 / " " " C 8 / " / " / " 7d " E & 6 TTTTTTTTTTT6 # ## 6 # # " 5% 6 " # " C # # ) ) 7 ! " D " "" " / / 5# % # 7 " ? ^ 6 * /## % d % - 5 [ % 57K 6 \7K7 < " 3 # + 57K 6 " % + ) T6 " * # # ! + " % % # % 5CK 6 % % ⋅ ⋅ " " ( # d C* * # " 5CK ) 7 7 d ⋅ ⋅ ⋅ " " " + 57K 6 5CK % % # % K " " % " % " * # " % + 57K 6 # % % " # 7K 7 # 6 % % 6 % % ) 7 % # " ⋅ ⋅ ⋅ " " " C Cd * 57K 6 " + # K 7 ) * 57K 6 5CK # 7C ( 8d , ) ) - , 7K # " C " * 7K7 < " * CK7 < " * C K7 < " *< # # 5 " " 5 *7 1 # " + ⋅ + " " / , 7 # ) ) 4 6 9 : 5 K7 < / " # " # - # 7K 6 ) ) -* ⋅ ⋅ + " " " # # # # ⋅ ⋅ ⋅ + " " " " " ^ ⋅ ⋅ ⋅ ⋅ = " " " " " ) " # # _ # % N ) ) - 7 % % \ " " * P ) ( ⋅ ⋅ ⋅ " " " " K7 < # # C 7 5 ) ) - 7K 6 ) ) 6 # * ^ , " 5 K 6 % F C " # % # 6 % % ⋅ ⋅ ⋅ ⋅ " " " " - 5CK 6 " # ) ) " 5 % # *. % % " # + ) % % ( ⋅ ⋅ ⋅ ⋅ " " " " 7C 8 % " 7 d % # K 5 " 6 L5 ) 6 : 5 8\ ) ) 7\C \ # - " " \^ 6 ' 5 C 6 " 7 * 6 2 \ e 2 : ' L 7 2 7K CK : 7K 7 K CK ' 7K 7 7CK 7 = K 7 7 K 7 L 7K7 < CK7 < C K7 < < K7 < 3 ) ) ' 7 - K7 < ( * 7K7 < 5# ' 7 * 6 * + " ⋅ + " " ⋅ ⋅ + " " " ⋅ ⋅ ⋅ + " " " " ⋅ ⋅ ⋅ ⋅ = " " " " " ) 5# " 6 , # ) ) ) ) # ⋅ − # - # 5 - L : 5 C K7 < 5 ( : = # 6 ) 6 ( 6 ) ) F7 ) ) ) ) - 5\ - - 6 S * + = ⋅ − = ⋅ − = ⋅ − = ⋅ − ⋅ − + ⋅ + ⋅ − + ⋅ − + ⋅ − = + − ⋅ + ⋅ − + ⋅ − = − " + − + = ⋅ ⋅ − − (" + + = − = − " - − " + − + − " + (" + − (" + − + − " − " + − " − " − " 51 )) # # E6 , % ) # " % " ) ) ># 9 C ?6 ^ & % ) ) - 5 >C " # # " # ? >; " # > ? ? & 7 # C P T + − " − " , 7 ) & "" ) ) " & J ) ) % - % # # " "" % # ) ) 5 < - " # 6 : 7 ^ )) , D # % C : 4 & )) ) # ## E # 1 $ ) " * # 7 . # " + % 5 ) # M . " 3 C 5 " : % " 6 5 5^ 6 " * = "" ) ) D 6 ) )))" )))" " " )))" )))" " )))" " " " " " " (" (" (" " " " X7Y * 6 ) - / 5" " W = 7 : 6 * ( )- ) ≈ ) - ) ( ($$ % " -" &" # 7 (; ' )) , " , N 5 5 " " # : ) " 6 # # " 1 >3 ) # % 2 " R # % ) W ) 3 + &" ) ) W 3 + " ) ) - % " % # ) " " 5 ) " % " $ # !# + " # # # ) % 7K 6 ) % % # % , " " % ) " # % ? " " # # W ) " * ) ) # - # # ) % "" " # * % > ) ( N1 ∞6∞N "" ? % # T + )" ) % " ) ) ( "" ) ) 5) 7K ; # $ 1 8 # % " 1 % - # " D # ; "" # : 3 ( ) # % D ) # 5 # )) D " 7K G # " ) 5 # " N6 . 7 - : 6 % % < % 7 + 6 S 5 % 9 ; 6* 8CC= 8< % # # )) # " G$ % ) ) + W W θ= " 76 # , ≤α ≤θ ? # % G , α " 7 " 5 + W /( 6 ) " " = −( ( L /α) " " % "" −( " " /α) > ( # " /α < 5 # > 3 > 6 α ∈ ( 7α ) α ∈ ( 7θ ) 1 ) ) # 5 = 1 + / ) 7 ( )= /( 6 /( 6 /( 6 ) ) ) " +" + / & →∞ − − →∞ , # + / /( 6 /( 6 − )= ) − # ) % # G ;, " # W # - = & " # 7 # > 6% (∞) = " )) 6 % # ) ) < /( 6 % = α - " 6 α ∈ ( 7θ ≡ 6 # 5 # " →∞ 5 6 = 7 * ) C /( 6 ) π 6 " = = /( ) π6 ( ( )= E ) ) - " E : ) # % ! )) 7 )) " " Q ) ) " 5= ∞6 $ # " ## "+ # " )) 6 < K # ) α - ( )= < W % < 6 # ( # 7π 6 ) ) "" 5 "" T6 6 < W % α <α # /( 6 π6 ( )= - < 7 " - < α & # # % < 6 3F1 : " 7 * L C 7 % L % L % L % L C L % % 8 L 8 % = L = % < L < % 7 L 7 3 # G # % N % & & % # W X7 Y # % / W )) # # # < $ % * % *% % " X<Y ; (; = $% # = = ( 7 , * < L% * = ∗ ∗ < ∗ ∗ < ' # ( < ( "" = ∗ ∗ ∗ ∗ ∗ ∗ " * ( L < = + ( ( <K < = < ( ∗ / 3 ,& ∗ ( (- () (" ( ( (( ( ∗ ∗ ∗ ∗ ∗ ∗ ∗ (- () (" ( ( (( ( ( = + 3 < $ = = ( ∗ ( * =( L% 8 ( E ' E 1 1( ' G# +,, / H 5 6 6 " - " )) $ L 9 # ( L ) , ( U # * = U / % ) " # 5 5 = I ℜ $ " " " ' ( _ =ϑ U UKU . " * 6 "" " # % % " 6$ % )) % # # # _ L% ) 1 5" $ 6* # " ∈ µ U • = / ϑ 8ℜ → ℜ ( < µ( • (ℜ ) → [ 7 ∞] µ8 -* ∑ ∈ )< ∞ ) µ (ϑ ( )) = µ ( ) / / # ) ( ) @ # ) ℜ " • . 5 # # ( ϑ 7 K7 ϑ ( )Uϑ ( )UKUϑ ( ) 6 5 ) 5 * = : # 7K7 " # _6* & # 6 $ # $ # ) # ) L # # " " * " = ⊂[ 7 ) ( ! ) [ 7 )= U ∈ # % # )= µ( ) > µ( µ( # )) ∑ µ( ) ∈ µ ([ 7 )) = µ ([ 7 )) = ∞ # )) / # )) * ∈ = )N ℜ ? )) = ∑ µ ( ) µ ([ 7 / ># 1 % # % # ' % 3 # 3 )) )) # ( " # )) ( % ) " ( - 5 # " ( % # " ( " ( % 3 ) " # % " " " * $ 6 - # ) L N [ 7 ]× [ 7 ] ∈ ℜ " # [ 7 ]× [ 7 ] = ([ 7 ]× [ 7 ])U ([ 7 ]× [ 7 ]) / % # L % " % # % ( " # " # " " L {}× [ 7 ]N " L % > ? # ) # ) L # > ? $ ( H "" % " & " ( % ' )) ( 6 9 ## L " " ) % # 5 S $ ) ) ( & # ) ) $ # ) ) > / ? # " # ( _ < I % , & # ' 7 ∈ℜ f 7 K7 f L ( = − =ϑ UKU L% 6 ϑ 7K7ϑ # " ( )UKUϑ ( ) 7 ϑ I ) 5 ) ( )I ϑ ( ) ( J # W % " " $ " L 2 # " % " % " + " 9 % # J % # " # " # $ + ) )) % # $ % " 6 % " 5 " " $ " ) " " " "" $ " W " W # H # " H , # # # 5 & " 1 # + # " + # # 6$ # # W & * $ % * % " & G N "" 3 # " # ! # 5 6 1W " # JJ$ & # & # # % , ) # W 3 ( " ( A ) 5 6 N ) _ / + = % + = # 1 # E " ( ) = ∑ [ (α ) ∗ ( )] $ ' α " W " %%%% " " :A ! (π ) = & # * ( )= ( π)= "; 3 ( ) W # π / % ' " % π π # ' +++ ' $ " % ' A+ 5 " 2 % " ) " $ - % $ H " H " # H H '6 $ " *# # " # & " # " " % 5 6 2 # % " % " " " " $ % W " ) # " " % π $ " " & % ( () # π 3 ) ) 7 " " # # ' ) - ## # # % %
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