A General Mass Transference Principle

Demi Allen; Simon Baker

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arXiv · 1803.02654

A General Mass Transference Principle

Demi Allen·Simon Baker

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Abstract

In this paper we prove a general form of the Mass Transference Principle for $\limsup$ sets defined via neighbourhoods of sets satisfying a certain local scaling property. Such sets include self-similar sets satisfying the open set condition and smooth compact manifolds embedded in $\mathbb{R}^n$. Our main result is applicable in locally compact metric spaces and allows one to transfer Hausdorff $g$-measure statements to Hausdorff $f$-measure statements. This work extends previous results of this type in several distinct directions.

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Demi Allen, Simon Baker. 2018-03-07. A General Mass Transference Principle. https://arxiv.org/abs/1803.02654

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