On selection theorems with decomposable values
Keywords
Multivalued mapping, continuous selection, decomposable value, Banach space, nonatomic probability measure, approximate partition, nerve of coveringAbstract
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.Downloads
Published
2000-06-01
How to Cite
1.
AGEEV, Sergei M. and REPOVŠ, Dušan. On selection theorems with decomposable values. Topological Methods in Nonlinear Analysis. Online. 1 June 2000. Vol. 15, no. 2, pp. 385 - 399. [Accessed 25 April 2024].
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