Sigma-porosity is separably determined

Abstract

We prove a separable reduction theorem for sigma-porosity of Suslin sets. In particular, if A is a Suslin subset in a Banach space X, then each separable subspace of X can be enlarged to a separable subspace V such that A is sigma-porous in X if and only if the intersection of A and V is sigma-porous in V. Such a result is proved for several types of sigma-porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem of L.Zajicek on differentiability of Lipschitz functions on separable Asplund spaces to the nonseparable setting.