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Date(投稿日時):Subject(見出し):From(投稿者):
25492009/03/13Re: 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)
25482009/03/13Re: f:R^2 $B"* (B[- $B!g (B, $B!g (B] $B$N;~ (B, $B"i (B_{R^2} f(x)dx= $B"i (B_0^{2 $B&P (B}( $B"i (B_0^ $B!g (B f(rcos( $B&U (B),rsin( $B&U (B))dr)d $B&U$r<($; (Bkyokoyoshida123@gmail.com
25472009/03/13Re: 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
25462009/03/13Re: $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
25452009/03/11Re: 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)
25442009/03/11Re: 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)
25432009/03/11Re: f:R^2→[-∞,∞]の時,∫_{R^2} f(x)dx=∫_0^{2π}(∫_0^∞ f(rcos(φ),rsin(φ))dr)dφを示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
25422009/03/09Re: 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
25412009/03/09Re: f:R^2 $B"* (B[- $B!g (B, $B!g (B] $B$N;~ (B, $B"i (B_{R^2} f(x)dx= $B"i (B_0^{2 $B&P (B}( $B"i (B_0^ $B!g (B f(rcos( $B&U (B),rsin( $B&U (B))dr)d $B&U$r<($; (Bkyokoyoshida123@gmail.com
25402009/03/09Re: $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
25392009/03/08Re: 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)
25382009/03/08Re: 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)
25372009/03/08Re: f:R^2→[-∞,∞]の時,∫_{R^2} f(x)dx=∫_0^{2π}(∫_0^∞ f(rcos(φ),rsin(φ))dr)dφを示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
25362009/03/08Re: f:R^2 $B"* (B[- $B!g (B, $B!g (B] $B$N;~ (B, $B"i (B_{R^2} f(x)dx= $B"i (B_0^{2 $B&P (B}( $B"i (B_0^ $B!g (B f(rcos( $B&U (B),rsin( $B&U (B))dr)d $B&U$r<($; (Bkyokoyoshida123@gmail.com
25352009/03/08Re: $B6K:BI8$rMQ$$$?6u4V$,40Hw (B& $B&RM-8B$K$J$kM}M3$O (B?kyokoyoshida123@gmail.com
25342009/03/08Re: X_1,X_2, $B!D (B,X_k $B$N@QB,EY$O=89gBN (BA={E_1 $B!_ (BE_2 $B!_!D!_ (BE_k;E_i $B": (BM_i} $B>e$N (Bpremeasure $B&L (B_0 $B$N3HD%$K$J$C$F$$$k;v$r3N$+$a$h (Bkyokoyoshida123@gmail.com
25332009/03/08Re: 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$$$k;v$r<($; (Bkyokoyoshida123@gmail.com
25322009/03/08Re: R^d $B!@ (B{0} $B$NG$0U$N3+=89g$O (BR_+ $B!_ (B S^{d-1} $B$N2D;;8D$NOB=89g$GI=$5$l$k;v$r<($; (Bkyokoyoshida123@gmail.com
25312009/03/08Re: $B&L (B $B$r (BBorel $BB,EY$H$9$k;~ (B, $B&L$,M-8B"N&W (B:f $B"* (BL(f)::= $B"i (B_a^b f(x)d $B&L (B(x) $B$O@~7AHF<LA|$r$J$9 (Bkyokoyoshida123@gmail.com
25302009/03/08Re: E $B$, (BA_{ $B&R&D (B} $B$N85$J$i (BE^{x_2} $B$O&L (B_1 $B2DB, (B. $B&L (B_1(E^{x_2}) $B$O&L (B_2 $B2DB, (B. $B99$K"i (B_{X_2} f(x_2)d $B&L (B_2(x)=lim[j $B"*!g (B] $B"i (B_{X_2}f_j(x_2)d $B&L (B_2(x)kyokoyoshida123@gmail.com
25292009/03/07Re: f:R^2→[-∞,∞]の時,∫_{R^2} f(x)dx=∫_0^{2π}(∫_0^∞ f(rcos(φ),rsin(φ))dr)dφを示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
25282009/03/07Re: 極座標を用いた空間が完備&σ有限になる理由は?chiaki@kit.ac.jp (Tsukamoto Chiaki)
25272009/03/07Re: EがA_{σδ}の元ならE^{x_2}はμ_1可測.μ_1(E^{x_2})はμ_2可測.更に∫_{X_2} f(x_2)dμ_2(x)=lim[j→∞]∫_{X_2}f_j(x_2)dμ_2(x)chiaki@kit.ac.jp (Tsukamoto Chiaki)
25262009/03/07Re: E $B$, (BA_{ $B&R&D (B} $B$N85$J$i (BE^{x_2} $B$O&L (B_1 $B2DB, (B. $B&L (B_1(E^{x_2}) $B$O&L (B_2 $B2DB, (B. $B99$K"i (B_{X_2} f(x_2)d $B&L (B_2(x)=lim[j $B"*!g (B] $B"i (B_{X_2}f_j(x_2)d $B&L (B_2(x)kyokoyoshida123@gmail.com
25252009/03/07Re: f:R^2 $B"* (B[- $B!g (B, $B!g (B] $B$N;~ (B, $B"i (B_{R^2} f(x)dx= $B"i (B_0^{2 $B&P (B}( $B"i (B_0^ $B!g (B f(rcos( $B&U (B),rsin( $B&U (B))dr)d $B&U$r<($; (Bkyokoyoshida123@gmail.com
25242009/03/07Re: $B6K:BI8$rMQ$$$?6u4V$,40Hw (B& $B&RM-8B$K$J$kM}M3$O (B?
↑ リクエストされた記事		kyokoyoshida123@gmail.com
25232009/03/07Re: ∫_(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)
25222009/03/07Re: f:R^2→[-∞,∞]の時,∫_{R^2} f(x)dx=∫_0^{2π}(∫_0^∞ f(rcos(φ),rsin(φ))dr)dφを示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
25212009/03/07Re: 極座標を用いた空間が完備&σ有限になる理由は?chiaki@kit.ac.jp (Tsukamoto Chiaki)
25202009/03/06f:R^2→[-∞,∞]の時,∫_{R^2} f(x)dx=∫_0^{2π}(∫_0^∞ f(rcos(φ),rsin(φ))dr)dφを示せkyokoyoshida123@gmail.com
25192009/03/06Re: $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
25182009/03/06極座標を用いた空間が完備&σ有限になる理由は?kyokoyoshida123@gmail.com
25172009/03/05Re: f(x_1,x_2)がμ_1×μ_2可積ならa.e.x_2∈X_2でf(x_1,x_2)はμ_1可積chiaki@kit.ac.jp (Tsukamoto Chiaki)
25162009/03/05Re: 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)
25152009/03/05Re: 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)
25142009/03/05Re: f(x_1,x_2) $B$,&L (B_1 $B!_&L (B_2 $B2D@Q$J$i (Ba.e.x_2 $B": (BX_2 $B$G (Bf(x_1,x_2) $B$O&L (B_1 $B2D@Q (Bkyokoyoshida123@gmail.com
25132009/03/05Re: 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
25122009/03/05Re: 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
25112009/03/05Re: 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)
25102009/03/05Re: 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)
25092009/03/05Re: 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)
25082009/03/05Re: X_1,X_2, $B!D (B,X_k $B$N@QB,EY$O=89gBN (BA={E_1 $B!_ (BE_2 $B!_!D!_ (BE_k;E_i $B": (BM_i} $B>e$N (Bpremeasure $B&L (B_0 $B$N3HD%$K$J$C$F$$$k;v$r3N$+$a$h (Bkyokoyoshida123@gmail.com
25072009/03/04Re: R^d=R^{d_1} $B!_ (BR^{d_2} $B$H$9$k;~ (B,R^d $B$N%k%Y!<%0B,EY (Bm $B$O (Bm_1 $B!_ (Bm_2 $B$N40Hw2=$K$J$C$F$$$k;v$r<($; (Bkyokoyoshida123@gmail.com
25062009/03/04Re: $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
25052009/03/03Re: 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)
25042009/03/03Re: 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)
25022009/03/03Re: f(x_1,x_2)がμ_1×μ_2可積ならa.e.x_2∈X_2でf(x_1,x_2)はμ_1可積chiaki@kit.ac.jp (Tsukamoto Chiaki)
25012009/03/03Re: X_1,X_2, $B!D (B,X_k $B$N@QB,EY$O=89gBN (BA={E_1 $B!_ (BE_2 $B!_!D!_ (BE_k;E_i $B": (BM_i} $B>e$N (Bpremeasure $B&L (B_0 $B$N3HD%$K$J$C$F$$$k;v$r3N$+$a$h (Bkyokoyoshida123@gmail.com
25002009/03/03Re: $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
24992009/03/03f(x_1,x_2)がμ_1×μ_2可積ならa.e.x_2∈X_2でf(x_1,x_2)はμ_1可積kyokoyoshida123@gmail.com
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