Some Properties of Variational Measures

Abstract

Recently several authors have established a remarkable property of the variational measures associated with a function. Expressed in classical language, this property asserts that if a function is ACG${}_*$ on all sets of Lebesgue measure zero then the function must be globally ACG${}_*$. This article is an exposition of some ideas related to this property with the intention of bringing it to the attention of a wider audience than these original papers might attract.