Aspects of area formulas by way of Luzin, Rad\'o, and Reichelderfer on metric measure spaces

TL;DR

This paper investigates measure-theoretic properties of Sobolev-type functions on metric measure spaces with Poincaré inequalities and doubling measures, focusing on area formulas and their implications.

Contribution

It extends classical area formulas to Sobolev functions on metric measure spaces, providing new insights into measure-theoretic properties in this setting.

Findings

Established measure-theoretic properties related to area formulas

Extended classical results to metric measure spaces with Poincaré inequality

Provided conditions under which area formulas hold in this context

Abstract

We consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit a Poincar\'e inequality and are equipped with a doubling measure. The properties we have selected to study are those that are related to area formulas.