%0 Journal Article
%T Profile decomposition for sequences of Borel measures
%A Mihai Mari£¿
%J Mathematics
%D 2014
%I arXiv
%X We prove that, if dichotomy occurs when the concentration-compactness principle is used, the dichotomizing sequence can be choosen so that a nontrivial part of it concentrates. Iterating this argument leads to a profile decomposition for arbitrary sequences of bounded Borel measures. To illustrate our results we give an application to the structure of bouded sequences in the Sobolev space $ W^{1, p}(\R^N)$.
%U http://arxiv.org/abs/1410.6125v1