A general principle for Hausdorff measure

TL;DR

This paper presents a broad principle for analyzing the Hausdorff measure of limsup sets, unifying and extending existing results like the Mass Transference Principle.

Contribution

It introduces a general framework that encompasses and generalizes the Mass Transference Principle for Hausdorff measures.

Findings

Unifies various results on Hausdorff measure of limsup sets

Extends the Mass Transference Principle to a broader context

Provides a new tool for studying measure-theoretic properties of limsup sets

Abstract

We introduce a general principle for studying the Hausdorff measure of limsup sets. A consequence of this principle is the well-known Mass Transference Principle of Beresnevich and Velani (2006).