Mass Transference Principle: From Balls to Arbitrary Shapes

The mass transference principle, proved by Beresnevich and Velani in 2006, is a strong result that gives lower bounds for the Hausdorff dimension of limsup sets of balls. We present a version for limsup sets of open sets of arbitrary shape.

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Bibliographic Details
Published in:International mathematics research notices 2021-04, Vol.2021 (8), p.6315-6330
Main Authors: Koivusalo, Henna, Rams, Michał
Format: Article
Language:English
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Summary:The mass transference principle, proved by Beresnevich and Velani in 2006, is a strong result that gives lower bounds for the Hausdorff dimension of limsup sets of balls. We present a version for limsup sets of open sets of arbitrary shape.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnz352