Published Paper

Inserted: 16 may 2017
Last Updated: 16 may 2017

Journal: Israel Journal of Mathematics
Volume: 196
Number: 1
Pages: 435-460
Year: 2012

Abstract:

Let n>2 and X be a Banach space of dimension strictly greater than n. We show there exists a directionally porous set P in X for which the set of C¹ surfaces of dimension n meeting P in positive measure is not meager. If X is separable this leads to a decomposition of X into a countable union of directionally porous sets and a set which is null on residually many C¹ surfaces of dimension n. This is of interest in the study of certain classes of null sets used to investigate differentiability of Lipschitz functions on Banach spaces.