This is an announcement for the paper "Surfaces meeting porous sets in positive measure" by Gareth Speight.
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 C^1 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 C^1 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.
Archive classification: math.FA math.CA math.MG
Mathematics Subject Classification: 28A75, 46T99, 46G99
Submitted from: G.Speight@Warwick.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.2376
or