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arXiv · 1308.6420

Avoiding σ-porous sets in Hilbert spaces

Michael Dymond
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Abstract

We give a constructive proof that any $σ$-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.

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Michael Dymond. 2013-12-14. Avoiding σ-porous sets in Hilbert spaces. https://arxiv.org/abs/1308.6420

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