On selection theorems with decomposable values
Słowa kluczowe
Multivalued mapping, continuous selection, decomposable value, Banach space, nonatomic probability measure, approximate partition, nerve of coveringAbstrakt
The main result of the paper asserts that for every separable measurable space $(T,\mathfrak F,\mu)$, where $\mathfrak F$ is the $\sigma$-algebra of measurable subsets of $T$ and $\mu$ is a nonatomic probability measure on $\mathfrak F$, every Banach space $E$ and every paracompact space $X$, each dispersible closed-valued mapping $F: x \rightsquigarrow L_1(T,E)$ of $X$ into the Banach space $L_1(T,E)$ of all Bochner integrable functions $u: T\to E$, admits a continuous selection. Our work generalizes some results of Gon\v carov and Tol'stonogov.Pobrania
Opublikowane
2000-06-01
Jak cytować
1.
AGEEV, Sergei M. & REPOVŠ, Dušan. On selection theorems with decomposable values. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2000, T. 15, nr 2, s. 385–399. [udostępniono 22.7.2024].
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