Some deviation inequalities

TL;DR: In this article, a concentration property called Property~($\scriptstyle{R^n}$ was introduced for probability measures, which has an interesting stability under products and contractions.

Abstract: We introduce a concentration property for probability measures on $\scriptstyle{R^n}$, which we call Property~($\scriptstyle\tau$); we show that this property has an interesting stability under products and contractions (Lemmas 1,~2,~3). Using property~($\scriptstyle\tau$), we give a short proof for a recent deviation inequality due to Talagrand. In a third section, we also recover known concentration results for Gaussian measures using our approach.}