This is an announcement for the paper "Szlenk indices of convex hulls" by Gilles Lancien, Antonin Prochazka, and Matias Raja. Abstract: We study the general measures of non compactness defined on subsets of a dual Banach space, their associated derivations and their $\omega$-iterates. We introduce the notion of convexifiable measure of non compactness and investigate the properties of its associated fragment and slice derivations. We apply our results to the Kuratowski measure of non compactness and to the study of the Szlenk index of a Banach space. As a consequence, we obtain, for any countable ordinal $\alpha$, a characterization of the Banach spaces with Szlenk index bounded by $\omega^{\alpha+1}$ in terms of the existence an equivalent renorming. This extends a result by Knaust, Odell and Schlumprecht on Banach spaces with Szlenk index equal to $\omega$. Archive classification: math.FA Mathematics Subject Classification: 46B20 Submitted from: gilles.lancien@univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1504.06997 or http://arXiv.org/abs/1504.06997