# Multifunctions determined by integrable functions

## TL;DR

This paper explores the integral properties of multifunctions generated by vector-valued functions, highlighting how different integrability notions influence their behavior and providing insights into their roles as examples or counterexamples.

## Contribution

It analyzes how various integrability concepts apply to multifunctions derived from vector functions, clarifying their relationships and limitations.

## Key findings

- Bochner, McShane, Birkhoff integrability transfer to multifunctions
- Henstock integrability does not guarantee similar properties
- Multifunctions serve as useful examples and counterexamples

## Abstract

Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee it.