Surfaces Meeting Porous Sets in Positive Measure
Functional Analysis
2014-08-29 v2 Classical Analysis and ODEs
Metric Geometry
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.
Keywords
Cite
@article{arxiv.1201.2376,
title = {Surfaces Meeting Porous Sets in Positive Measure},
author = {Gareth Speight},
journal= {arXiv preprint arXiv:1201.2376},
year = {2014}
}