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2022 A Mass Transference Principle and Sets with Large Intersections
Tomas Persson
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Real Anal. Exchange 47(1): 191-206 (2022). DOI: 10.14321/realanalexch.47.1.1619498208

Abstract

I prove a mass transference principle for general shapes, similar to a recent result by H. Koivusalo and M. Rams. The proof relies on Vitali's covering lemma and manipulations with Riesz energies.

The main novelty is that it is proved that the obtained limsup-set belongs to the classes of sets with large intersections, as defined by K. Falconer. This has previously not been proved for as general shapes as in this paper.

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Tomas Persson. "A Mass Transference Principle and Sets with Large Intersections." Real Anal. Exchange 47 (1) 191 - 206, 2022. https://doi.org/10.14321/realanalexch.47.1.1619498208

Information

Published: 2022
First available in Project Euclid: 13 June 2022

Digital Object Identifier: 10.14321/realanalexch.47.1.1619498208

Subjects:
Primary: 28A78 , 28A80

Keywords: Hausdorff dimension , Mass transference principle

Rights: Copyright © 2022 Michigan State University Press

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Vol.47 • No. 1 • 2022
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