English

Avoiding \sigma-porous sets in Hilbert spaces

Functional Analysis 2013-12-17 v2

Abstract

We give a constructive proof that any σ\sigma-porous subset of a Hilbert space has Lebesgue measure zero on typical C1C^{1} curves. Further, we discover that this result does not extend to all forms of porosity; we find that even power-pp porous sets may meet many C1C^{1} 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}
}
R2 v1 2026-06-22T01:17:14.597Z