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Date(投稿日時):Subject(見出し):From(投稿者):
24952009/03/02Re: 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)
24942009/03/02Re: 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
24932009/03/02Re: 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$$$k;v$r<($; (Bkyokoyoshida123@gmail.com
24922009/03/02Re: X_1,X_2, $B!D (B,X_k $B$N@QB,EY$O=89gBN (BA={E_1 $B!_ (BE_2 $B!_!D!_ (BE_k;E_i $B": (BM_i} $B>e$N (Bpremeasure $B&L (B_0 $B$N3HD%$K$J$C$F$$$k;v$r3N$+$a$h (Bkyokoyoshida123@gmail.com
24912009/03/02Re: $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
24902009/03/02Re: 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)
24892009/03/02Re: 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)
24882009/03/02Re: 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)
24872009/03/02Re: 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)
24862009/03/02Re: 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)
24852009/03/01Re: 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
24842009/03/01Re: E $B$,G$0U (B} $B$N85$J$i (BE^{x_2} $B$O (Ba.e. $B&L (B_1 $B2DB, (B. $B&L (B_1(E^{x_2}) $B$O (Ba.e. $B&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
24832009/03/01Re: 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$$$k;v$r3N$+$a$h (Bkyokoyoshida123@gmail.com
24822009/02/28Re: R^d=R^{d_1} $B!_ (BR^{d_2} $B$H$9$k;~ (B,R^d $B$N%k%Y!<%0B,EY (Bm $B$O (Bm_1 $B!_ (Bm_2 $B$N40Hw2=$K$J$C$F$$$k;v$r<($; (Bkyokoyoshida123@gmail.com
24812009/02/28Re: $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
24802009/02/26Re: 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)
24792009/02/26Re: E $B$,G$0U (B} $B$N85$J$i (BE^{x_2} $B$O (Ba.e. $B&L (B_1 $B2DB, (B. $B&L (B_1(E^{x_2}) $B$O (Ba.e. $B&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
24782009/02/26Re: 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$$$k;v$r3N$+$a$h (Bkyokoyoshida123@gmail.com
24772009/02/25Re: R^d＼{0}の任意の開集合はR_+ × S^{d-1}の可算個の和集合で表される事を示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
24762009/02/25Re: R^d=R^{d_1}×R^{d_2}とする時,R^dのルベーグ測度mはm_1×m_2の完備化になっている事を示せchiaki@kit.ac.jp (Tsukamoto Chiaki)
24752009/02/25Re: R^d $B!@ (B{0} $B$NG$0U$N3+=89g$O (BR_+ $B!_ (B S^{d-1} $B$N2D;;8D$NOB=89g$GI=$5$l$k;v$r<($; (Bkyokoyoshida123@gmail.com
24742009/02/25Re: R^d=R^{d_1} $B!_ (BR^{d_2} $B$H$9$k;~ (B,R^d $B$N%k%Y!<%0B,EY (Bm $B$O (Bm_1 $B!_ (Bm_2 $B$N40Hw2=$K$J$C$F$$$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)
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