A new version of the Dvoretzky-Rogers lemma
Ferenc Fodor · Open Collections · 2017
The Dvoretzky-Rogers lemma states the existence of a simplex of relatively large volume in a John decomposition of the identity. This theorem was the key ingredient in the recent proof by M. Nasz\'odi of a quantitative version of Helly's theorem which had been conjectured originally by B\'ar\'any, Katchalski and Pach. In this talk we present a new measure theoretic version of the Dvoretzky-Rogers lemma which provides information about the distribution of isotropic measures. This result is joint with K.J. B\"or\"oczky (Budapest) and D. Hug (Karlsruhe).