A dimensional mass transference principle for Borel probability measures and applications

Abstract

In this article, we establish a dimensional mass transference principle valid when the ambient measure is finite. We provide two applications of this result. First we study certain dynamical coverings associated with some self-similar IFS with overlaps and then we give an application in Diophantine approximation to rational approximation among points of $[0,1]$ with few digit equal to 1 in their base-3 expansion.