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On sup-measurability of multifunctions with some density properties

Kwiecińska G.

Demonstratio Mathematica

2012

Vol. 45, nr 4

821-833

The paper is concerned with sup measurability of a multifunction F defined on the product (…) of metric spaces with some differentiation bases. We introduce the lower (…) property and the upper (…) property of multifunction, where (…), and we prove sup measurabilty of F when it has the upper (…) property at (x, y) and F(x, ź) has the lower (…) property at y for every (…). Some application of this theorem to the existence of solutions of differential inclusions (…) is given.