Upper and lower Lebesgue classification of multivalued mappings of two variables

TL;DR

This paper introduces a new Lebesgue classification framework for multivalued mappings of two variables, providing results on their upper and lower classifications across various space classes.

Contribution

It develops a functional Lebesgue classification for multivalued mappings and establishes classification results for broad classes of spaces.

Findings

Established upper and lower Lebesgue classifications for multivalued mappings

Extended classification results to wide classes of spaces

Provided a new framework for analyzing multivalued mappings

Abstract

We introduce a functional Lebesgue classification of multivalued mappings and obtain results on upper and lower Lebesgue classifications of multivalued mappings $F:X\times Y\to Z$ for wide classes of spaces $X$, $Y$ and $Z$.