On sup-measurability of multifunctions with some density properties

Demonstratio mathematica

article

Grażyna Kwiecińska¹ 

[1] Institute of Mathematics

关键词: multifunctions;    density with respect to the differentiation basis;    approximate continuity;    superpositional measurability;    differential inclusions;   

DOI  :  10.1515/dema-2013-0422

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

The paper is concerned with sup-measurability of a multifunction F defined on the product X × Y of metric spaces with some differentiation bases. We introduce the lower D α property and the upper D α property of multifunction, where α ∈ (0, 1) ⊂ ℝ, and we prove sup-measurabilty of F when it has the upper D α property at ( x, y ), and F ( x , ·) has the lower D α property at y for every ( x, y ) ∈ X × Y . Some application of this theorem to the existence of solutions of differential inclusions f ′ ( x ) ∈ F ( x, f ( x )) is given.

【 授权许可】

CC BY