This is an announcement for the paper "Strengthening of weak convergence for Radon measures in separable Banach spaces" by E. Ostrovsky and L. Sirota. Abstract: We prove in this short report that for arbitrary weak converging sequence of sigma-finite Borelian measures in the separable Banach space there is a compact embedded separable subspace such that this measures not only are concentrated in this subspace but weak converge therein. Archive classification: math.FA Submitted from: leos@post.sce.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1505.06235 or http://arXiv.org/abs/1505.06235