On absolutely friendly measures on QSd$\mathbb {Q}_S^d$

Abstract

AbstractIn this paper, we extend the work of Pollington and Velani [Selecta Math. 11(2005)] to an ‐arithmetic set‐up, where is a finite set of valuations of . In particular, for an absolutely friendly measure supported on a compact set in , we give a summation condition on an approximating function such that almost no point in the compact set is approximable. The crucial ingredient is a version of the simplex lemma that we prove dynamically.