Mendelson, Shahar2016-03-152016-03-150002-9939http://hdl.handle.net/1885/100414We show that for any class of uniformly bounded functions H with a reasonable combinatorial dimension, the vast majority of small subsets of the n-dimensional combinatorial cube cannot be represented as a Lipschitz image of a subset of H, unless the Lipschitz constant is very large. We apply this result to the case when H consists of linear functionals of norm at most one on a Hilbert space.The author was supported in part by an Australian Research council Discovery grant.© 2006 American Mathematical Society2007-11-1410.1090/S0002-9939-06-08620-52016-06-14