# A Remark on an Integral Characterization of the Dual of BV

## TL;DR

This paper demonstrates that, assuming the continuum hypothesis, elements of the dual space of functions of bounded variation can be represented integrally using Lebesgue and Kolmogorov-Burkill integrals.

## Contribution

It provides an integral characterization of the dual of BV functions under the continuum hypothesis, linking dual elements to specific integral representations.

## Key findings

- Dual of BV functions can be represented via Lebesgue and Kolmogorov-Burkill integrals.
- Integral representation depends on the continuum hypothesis.
- Connects dual space elements to classical integral forms.

## Abstract

In this paper, we show how under the continuum hypothesis one can obtain an integral representation for elements of the topological dual of the space of functions of bounded variation in terms of Lebesgue and Kolmogorov-Burkill integrals.