Hausdorff dimension and capacities of compact sets

TL;DR

This paper provides a comprehensive proof linking the capacities of a measure to its Fourier transform, enhancing understanding of geometric measure theory.

Contribution

It offers a complete proof of the relationship between capacities of measures and their Fourier transforms, clarifying foundational aspects.

Findings

Capacities are expressed in terms of Fourier transforms.

The proof solidifies the theoretical connection in geometric measure theory.

Provides a basis for further research in Fourier analysis and capacity theory.

Abstract

We give a complete proof of the expression of capacities of a measure in terms of its Fourier transform.