Revisiting a theorem on multifunctions of one real variable

TL;DR

This paper revisits a classical theorem on multifunctions of one real variable, weakening its hypotheses and expanding its applicability to broader situations, with illustrative applications provided.

Contribution

It reformulates Theorem 2 of [3], relaxing assumptions and highlighting richer conclusions for wider use cases.

Findings

Broader applicability of the theorem demonstrated

Weakened hypotheses still yield meaningful conclusions

Applications showcased in various contexts

Abstract

In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range of different situations. Samples of such applications are also given.