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Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions. (English) Zbl 1114.28009

Let \(F:X\times Y\to Z\) be a multifunction defined on a product of Polish spaces, both of them endowed with regular Borel measures, and taking nonempty complete values in a separable metric space \(Z\). Conditions under which such \(F\) admits a selection whose \(X\)-sections are a.e.-continuous and \(Y\)-sections are measurable, are exhibited. An application of selections of this kind in the area of differential inclusions is mentioned.

MSC:

28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
54C65 Selections in general topology
34A60 Ordinary differential inclusions
26E25 Set-valued functions

Citations:

Zbl 0851.54021
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