Abstract of a paper by Gareth Speight
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 http://arXiv.org/abs/1201.2376
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alspach@math.okstate.edu