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Date(投稿日時):Subject(見出し):From(投稿者):
24762009/02/25Re: R^d=R^{d_1}×R^{d_2}とする時,R^dのルベーグ測度mはm_1×m_2の完備化になっている事を示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
24752009/02/25Re: R^d $B!@ (B{0} $B$NG$0U$N3+=89g$O (BR_+ $B!_ (B S^{d-1} $B$N2D;;8D$NOB=89g$GI=$5$l$k;v$r<($; (Bkyokoyoshida123@gmail.com
24742009/02/25Re: R^d=R^{d_1} $B!_ (BR^{d_2} $B$H$9$k;~ (B,R^d $B$N%k%Y!<%0B,EY (Bm $B$O (Bm_1 $B!_ (Bm_2 $B$N40Hw2=$K$J$C$F$$$k;v$r<($; (Bkyokoyoshida123@gmail.com
24732009/02/25Re: μ をBorel測度とする時, μが有限⇔ψ:f→L(f)::=∫_a^b f(x)dμ(x)は線形汎写像をなすchiaki@kit.ac.jp (Tsukamoto Chiaki)
24722009/02/24Re: $B&L (B $B$r (BBorel $BB,EY$H$9$k;~ (B, $B&L$,M-8B"N&W (B:f $B"* (BL(f)::= $B"i (B_a^b f(x)d $B&L (B(x) $B$O@~7AHF<LA|$r$J$9 (Bkyokoyoshida123@gmail.com
24712009/02/24Re: X_1,X_2,…,X_kの積測度は集合体A={E_1×E_2×…×E_k;E_i∈M_i}上のpremeasure μ_0の拡張になっている事を確かめよchiaki@kit.ac.jp (Tsukamoto Chiaki)
24702009/02/24Re: R^d=R^{d_1}×R^{d_2}とする時,R^dのルベーグ測度mはm_1×m_2の完備化になっている事を示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
24692009/02/24Re: Eが任意}の元ならE^{x_2}はa.e.μ_1可測.μ_1(E^{x_2})はa.e.μ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)chiaki@kit.ac.jp (Tsukamoto Chiaki)
24682009/02/24Re: Eが任意}の元ならE^{x_2}はa.e.μ_1可測.μ_1(E^{x_2})はa.e.μ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)chiaki@kit.ac.jp (Tsukamoto Chiaki)
24672009/02/24Re: Eが任意の元ならE^{x_2}はa.e.μ_1可測.μ_1(E^{x_2})はa.e.μ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)chiaki@kit.ac.jp (Tsukamoto Chiaki)
24662009/02/24Re: R^d＼{0}の任意の開集合はR_+ × S^{d-1}の可算個の和集合で表される事を示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
24652009/02/24Re: μ をBorel測度とする時, μが有限⇔ψ:f→L(f)::=∫_a^b f(x)dμ(x)は線形汎写像をなすchiaki@kit.ac.jp (Tsukamoto Chiaki)
24642009/02/24Re: f(x,y)をR×Rでルベーグ可測な非負関数とする。次の真偽を判定せよchiaki@kit.ac.jp (Tsukamoto Chiaki)
24632009/02/24Re: Eが任意}の元ならE^{x_2}はa.e.μ_1可測.μ_1(E^{x_2})はa.e.μ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)kyokoyoshida123@gmail.com
24622009/02/24Re: Eが任意}の元ならE^{x_2}はa.e.μ_1可測.μ_1(E^{x_2})はa.e.μ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)kyokoyoshida123@gmail.com
24612009/02/24Re: μ をBorel測度とする時, μが有限⇔ψ:f→L(f)::=∫_a^b f(x)dμ(x)は線形汎写像をなすkyokoyoshida123@gmail.com
24602009/02/23Eが任意}の元ならE^{x_2}はa.e.μ_1可測.μ_1(E^{x_2})はa.e.μ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)kyokoyoshida123@gmail.com
24592009/02/23Re: f(x,y) $B$r (BR $B!_ (BR $B$G%k%Y!<%02DB,$JHsIi4X?t$H$9$k!#<!$N??56$rH=Dj$;$h (Bkyokoyoshida123@gmail.com
24582009/02/22Re: EがA_{σδ}の元ならE^{x_2}はμ_1可測.μ_1(E^{x_2})はμ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)chiaki@kit.ac.jp (Tsukamoto Chiaki)
24572009/02/22X_1,X_2,…,X_kの積測度は集合体A={E_1×E_2×…×E_k;E_i∈M_i}上のpremeasure μ_0の拡張になっている事を確かめよkyokoyoshida123@gmail.com
24562009/02/22R^d=R^{d_1}×R^{d_2}とする時,R^dのルベーグ測度mはm_1×m_2の完備化になっている事を示せkyokoyoshida123@gmail.com
24552009/02/22R^d＼{0}の任意の開集合はR_+ × S^{d-1}の可算個の和集合で表される事を示せkyokoyoshida123@gmail.com
24542009/02/22Re: 4 $BCJ3,$G%k%Y!<%0@QJ,$r9=C[$;$h!# (Bkyokoyoshida123@gmail.com
24532009/02/22μ をBorel測度とする時, μが有限⇔ψ:f→L(f)::=∫_a^b f(x)dμ(x)は線形汎写像をなすkyokoyoshida123@gmail.com
24522009/02/21Re: E $B$, (BA_{ $B&R&D (B} $B$N85$J$i (BE^{x_2} $B$O&L (B_1 $B2DB, (B. $B&L (B_1(E^{x_2}) $B$O&L (B_2 $B2DB, (B. $B99$K"i (B_{X_2} f(x_2)d $B&L (B_2(x)=lim[j $B"*!g (B] $B"i (B_{X_2}f_j(x_2)d $B&L (B_2(x)kyokoyoshida123@gmail.com
24512009/02/19Re: EがA_{σδ}の元ならE^{x_2}はμ_1可測.μ_1(E^{x_2})はμ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)chiaki@kit.ac.jp (Tsukamoto Chiaki)
24502009/02/19Re: 4段階でルベーグ積分を構築せよ。chiaki@kit.ac.jp (Tsukamoto Chiaki)
24492009/02/19Re: E $B$, (BA_{ $B&R&D (B} $B$N85$J$i (BE^{x_2} $B$O&L (B_1 $B2DB, (B. $B&L (B_1(E^{x_2}) $B$O&L (B_2 $B2DB, (B. $B99$K"i (B_{X_2} f(x_2)d $B&L (B_2(x)=lim[j $B"*!g (B] $B"i (B_{X_2}f_j(x_2)d $B&L (B_2(x)kyokoyoshida123@gmail.com
24482009/02/18Re: E $B$, (BA_{ $B&R&D (B} $B$N85$J$i (BE^{x_2} $B$O&L (B_1 $B2DB, (B. $B&L (B_1(E^{x_2}) $B$O&L (B_2 $B2DB, (B. $B99$K"i (B_{X_2} f(x_2)d $B&L (B_2(x)=lim[j $B"*!g (B] $B"i (B_{X_2}f_j(x_2)d $B&L (B_2(x)kyokoyoshida123@gmail.com
24472009/02/18Re: 4 $BCJ3,$G%k%Y!<%0@QJ,$r9=C[$;$h!# (Bkyokoyoshida123@gmail.com
24462009/02/16Re: ∫_(R^d)|f(x)|dx=∫[0..∞]m(E_α)dα(但し,mはルベーグ測度)となる事示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
24452009/02/16Re: EがA_{σδ}の元ならE^{x_2}はμ_1可測.μ_1(E^{x_2})はμ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)chiaki@kit.ac.jp (Tsukamoto Chiaki)
24442009/02/16Re: 4段階でルベーグ積分を構築せよ。chiaki@kit.ac.jp (Tsukamoto Chiaki)
24432009/02/15Re: $B"i (B_(R^d)|f(x)|dx= $B"i (B[0.. $B!g (B]m(E_ $B&A (B)d $B&A (B ( $BC"$7 (B,m $B$O%k%Y!<%0B,EY (B) $B$H$J$k;v<($; (Bkyokoyoshida123@gmail.com
24422009/02/15Re: f(x,y)をR×Rでルベーグ可測な非負関数とする。次の真偽を判定せよchiaki@kit.ac.jp (Tsukamoto Chiaki)
24412009/02/15Re: f(x,y)をR×Rでルベーグ可測な非負関数とする。次の真偽を判定せよchiaki@kit.ac.jp (Tsukamoto Chiaki)
24402009/02/15Re: f(x,y) $B$r (BR $B!_ (BR $B$G%k%Y!<%02DB,$JHsIi4X?t$H$9$k!#<!$N??56$rH=Dj$;$h (Bkyokoyoshida123@gmail.com
24392009/02/15Re: f(x,y) $B$r (BR $B!_ (BR $B$G%k%Y!<%02DB,$JHsIi4X?t$H$9$k!#<!$N??56$rH=Dj$;$h (Bkyokoyoshida123@gmail.com
24382009/02/14Re: f(x,y) $B$r (BR $B!_ (BR $B$G%k%Y!<%02DB,$JHsIi4X?t$H$9$k!#<!$N??56$rH=Dj$;$h (Bkyokoyoshida123@gmail.com
24372009/02/14EがA_{σδ}の元ならE^{x_2}はμ_1可測.μ_1(E^{x_2})はμ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)kyokoyoshida123@gmail.com
24362009/02/134段階でルベーグ積分を構築せよ。kyokoyoshida123@gmail.com
24352009/02/13Re: A $B$O=89gBN (B,M:= $B&R (B(A) $B$G&L$O (Bpremeasure $B$+$i3HD%$5$l$?B,EY (B. $B&L$,&RM-8B$J$i&L$O0l0UE*$KB8:_$9$k (Bkyokoyoshida123@gmail.com
24342009/02/10Re: Aは集合体,M:=σ(A)でμはpremeasureから拡張された測度.μがσ有限ならμは一意的に存在するchiaki@kit.ac.jp (Tsukamoto Chiaki)
24332009/02/10Re: A $B$O=89gBN (B,M:= $B&R (B(A) $B$G&L$O (Bpremeasure $B$+$i3HD%$5$l$?B,EY (B. $B&L$,&RM-8B$J$i&L$O0l0UE*$KB8:_$9$k (Bkyokoyoshida123@gmail.com
24322009/02/09Re: Aは集合体,M:=σ(A)でμはpremeasureから拡張された測度.μがσ有限ならμは一意的に存在するchiaki@kit.ac.jp (Tsukamoto Chiaki)
24312009/02/09Aは集合体,M:=σ(A)でμはpremeasureから拡張された測度.μがσ有限ならμは一意的に存在するkyokoyoshida123@gmail.com
24302009/02/09Re: E $B$, (BCaratheodory $B2DB,"N (BE $B$O (BLebesgue $B2DB, (Bkyokoyoshida123@gmail.com
24292009/02/07Re: EがCaratheodory可測⇔EはLebesgue可測chiaki@kit.ac.jp (Tsukamoto Chiaki)
24282009/02/07Re: E $B$, (BCaratheodory $B2DB,"N (BE $B$O (BLebesgue $B2DB, (Bkyokoyoshida123@gmail.com
24272009/02/07Re: Borel $BB,EY$,M-8BH>7B5e$GM-8B$J$i&L (B(O $B!@ (BE)< $B&E (B, $B&L (B(E $B!@ (BF)< $B&E$G (BF $B"> (BE $B"> (BO $B$J$k (B, $B3+JD=89g (BO $B$H (BF $B$,<h$l$k (Bkyokoyoshida123@gmail.com
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