Geodesic
The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 429-437

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We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil, $\int _R{\mathrm d}\alpha (t) f(t)$, where $R$ is a compact interval of $\mathbb{R}^n$, $\alpha $ and $f$ are functions with values on $L(Z,W)$ and $Z$ respectively, and $Z$ and $W$ are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral, $\int _R\alpha (t)\mathrm{d}f(t)$, as well as to unbounded intervals $R$.
We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil, $\int _R{\mathrm d}\alpha (t) f(t)$, where $R$ is a compact interval of $\mathbb{R}^n$, $\alpha $ and $f$ are functions with values on $L(Z,W)$ and $Z$ respectively, and $Z$ and $W$ are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral, $\int _R\alpha (t)\mathrm{d}f(t)$, as well as to unbounded intervals $R$.
Classification : 26A39, 26A42, 28B05
Keywords: Monotone Convergence Theorem; Kurzweil vector integral; ordered normed spaces 
Federson, Márcia. The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 429-437. http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a17/
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     title = {The monotone convergence theorem for multidimensional abstract {Kurzweil} vector integrals},
     journal = {Czechoslovak Mathematical Journal},
     pages = {429--437},
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     volume = {52},
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     mrnumber = {1905449},
     zbl = {1022.28003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a17/}
}
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