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Date(投稿日時):Subject(見出し):From(投稿者):
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
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