Avoiding \sigma-porous sets in Hilbert spaces
Functional Analysis
2013-12-17 v2
Abstract
We give a constructive proof that any -porous subset of a Hilbert space has Lebesgue measure zero on typical curves. Further, we discover that this result does not extend to all forms of porosity; we find that even power- porous sets may meet many curves in positive measure.
Keywords
Cite
@article{arxiv.1308.6420,
title = {Avoiding \sigma-porous sets in Hilbert spaces},
author = {Michael Dymond},
journal= {arXiv preprint arXiv:1308.6420},
year = {2013}
}