An area formula in metric spaces

TL;DR

This paper introduces an area formula for continuous functions between metric spaces that relies on a measure-theoretic Jacobian, avoiding the need for differentiability.

Contribution

It provides a novel area formula in metric spaces using a measure-theoretic Jacobian without assuming differentiability.

Findings

Establishes an area formula for continuous maps in metric spaces

Defines a measure-theoretic Jacobian as the density of a pull-back measure

Applies minimal regularity assumptions

Abstract

We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure theoretic notion of Jacobian, defined as the density of a suitable "pull-back measure".