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arXiv · 2107.13730

Random multifunctions as the set minimizers of infinitely many differentiable random functions

Juan Guillermo Garrido·Pedro Pérez-Aros·Emilio Vilches
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Abstract

Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers of an infinitely many differentiable normal integrand, which preserves the convexity of the random multifunction. We provide several applications of this result to the approximation of random multifunctions and integrands. The paper ends with a characterization of the set of integrable selections of a measurable multifunction as the set of minimizers of an infinitely many differentiable integral function.

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Juan Guillermo Garrido, Pedro Pérez-Aros, Emilio Vilches. 2021-07-29. Random multifunctions as the set minimizers of infinitely many differentiable random functions. https://arxiv.org/abs/2107.13730

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