Avoiding σ-porous sets in Hilbert spaces
Abstract
We give a constructive proof that any σ-porous subset of a Hilbert space has Lebesgue measure zero on typical C1 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 C1 curves in positive measure.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.