# Mass transference principle: from balls to arbitrary shapes

## TL;DR

This paper extends the mass transference principle to apply to limsup sets of open sets with arbitrary shapes, broadening its applicability beyond balls.

## Contribution

It introduces a generalized version of the mass transference principle for open sets of arbitrary shape, expanding the scope of the original theorem.

## Key findings

- Generalization of the mass transference principle to arbitrary shapes
- Provides lower bounds for Hausdorff dimension of limsup sets of open sets
- Broadens the applicability of the original result

## Abstract

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.