A pointwise characterization of functions of bounded variation on metric spaces

TL;DR

This paper introduces a novel pointwise inequality-based characterization of functions of bounded variation that applies to both Euclidean and general metric spaces, expanding understanding of BV functions.

Contribution

It provides a new, more general pointwise characterization of BV functions that is valid in metric spaces, including Euclidean spaces, which was not previously known.

Findings

New pointwise inequality characterizes BV functions.

Applicable to Euclidean and general metric spaces.

Advances understanding of functions of bounded variation.

Abstract

We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in general metric spaces.