naa a22 4500 510783031 CHVBK 20180411083253.0 cr unu---uuuuu 180411e20130801xx s 000 0 eng 10.1007/s11856-012-0171-4 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0171-4 Speight Gareth Mathematics Institute, Zeeman Building University of Warwick, CV4 7AL, Coventry, England aut Surfaces meeting porous sets in positive measure [Elektronische Daten] [Gareth Speight] Let X be a Banach space and 2 < n < dimX. 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 the union of a σ-directionally porous set and a set which is null on residually many C 1 surfaces of dimension n. This is of interest in the study of Γn-null and Γ-null sets and their applications to differentiability of Lipschitz functions. Hebrew University Magnes Press, 2013 Israel Journal of Mathematics Springer US; http://www.springer-ny.com 196/1(2013-08-01), 435-460 0021-2172 196:1<435 2013 196 11856 https://doi.org/10.1007/s11856-012-0171-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0171-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Speight Gareth Mathematics Institute, Zeeman Building University of Warwick, CV4 7AL, Coventry, England aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 196/1(2013-08-01), 435-460 0021-2172 196:1<435 2013 196 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer