Let (T,F,μ) be a separable probability measure space with a nonatomic measure μ. A subset K ⊂ L(T,Rⁿ) is said to be decomposable if for every A ∈ F and f ∈ K, g ∈ K one has . Using the property of decomposability as a substitute for convexity a relaxation theorem for fixed point sets of set-valued function is given.
@article{bwmeta1.element.bwnjournal-article-div16i1n5bwm,
author = {Andrzej Kisielewicz},
title = {Relaxation theorem for set-valued functions with decomposable values},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {16},
year = {1996},
pages = {91-97},
zbl = {0867.54025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-div16i1n5bwm}
}
Andrzej Kisielewicz. Relaxation theorem for set-valued functions with decomposable values. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 16 (1996) pp. 91-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div16i1n5bwm/
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