Inserted: 16 may 2017
Last Updated: 16 may 2017
Journal: Israel Journal of Mathematics
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.