Michael Dymond
Published 2013-08-29, updated 2013-12-14Version 2
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.
Multipliers on Hilbert spaces of functions on R
A constructive proof of the Dvoretzky--Rogers Theorem in $\ell_{p}$ spaces
Frames of subspaces in Hilbert spaces with $W$-metrics
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