## 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

### Keywords:

lower semicontinuity

Zbl 0851.54021
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