The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals
Czechoslovak Mathematical Journal (2002)
- Volume: 52, Issue: 2, page 429-437
- ISSN: 0011-4642
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topFederson, Márcia. "The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals." Czechoslovak Mathematical Journal 52.2 (2002): 429-437. <http://eudml.org/doc/30712>.
@article{Federson2002,
abstract = {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 $R$.},
author = {Federson, Márcia},
journal = {Czechoslovak Mathematical Journal},
keywords = {Monotone Convergence Theorem; Kurzweil vector integral; ordered normed spaces; monotone convergence theorem; Kurzweil vector integral; ordered normed spaces},
language = {eng},
number = {2},
pages = {429-437},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals},
url = {http://eudml.org/doc/30712},
volume = {52},
year = {2002},
}
TY - JOUR
AU - Federson, Márcia
TI - The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 2
SP - 429
EP - 437
AB - 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 $R$.
LA - eng
KW - Monotone Convergence Theorem; Kurzweil vector integral; ordered normed spaces; monotone convergence theorem; Kurzweil vector integral; ordered normed spaces
UR - http://eudml.org/doc/30712
ER -
References
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