A dimensional mass transference principle for Borel probability measures and applications

Édouard Daviaud (1)

1 UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12

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.

Mots clés: Mass transference principles; ubiquity; self-similarity; Diohantine approximation

Domaines: Géométrie métrique [math.MG]

Édouard Daviaud. A dimensional mass transference principle for Borel probability measures and applications. 2023. ⟨hal-03626178v2⟩