D-measurability and t-Wright convex functions

TL;DR

This paper proves that t-Wright convex functions bounded above on certain measurable sets are continuous, addressing a problem posed by Baron and Ger and building on prior research.

Contribution

It establishes the continuity of t-Wright convex functions under boundedness conditions on D-measurable non-Haar meager sets, advancing understanding in convex analysis.

Findings

t-Wright convex functions bounded on D-measurable non-Haar meager sets are continuous

Addresses a problem posed by Baron and Ger

Builds on prior work by Olbrys and Jablonska

Abstract

In the paper we will prove that each t-Wright convex function, which is bounded above on a D-measurable non-Haar meager set is continuous. Our paper refers to papers \cite{Olbrys}, \cite{Jablonska} and a problem posed by K.Baron and R.Ger.