On Measure Concentration of Vector-Valued Maps
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 261-278
MSC: Primary 60E15.
DOI: 10.4064/ba55-3-7
Abstract
We study concentration properties for vector-valued maps. In particular, we describe inequalities which capture the exact dimensional behavior of Lipschitz maps with values in $\mathbb R^{k}$. To this end, we study in particular a domination principle for projections which might be of independent interest. We further compare our conclusions with earlier results by Pinelis in the Gaussian case, and discuss extensions to the infinite-dimensional setting.
