This is an announcement for the paper "Avoiding sigma-porous sets in Hilbert spaces" by Michael Dymond.

Abstract: We give a constructive proof that any $\sigma$-porous subset of a Hilbert space has Lebesgue measure zero on typical $C^{1}$ curves. Further, we discover that this result does not extend to all forms of porosity; we find that even power-$p$ porous sets may meet many $C^{1}$ curves in positive measure.

Archive classification: math.FA

Submitted from: dymondm@maths.bham.ac.uk

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1308.6420

or

http://arXiv.org/abs/1308.6420