Avoiding sigma-porous sets in Hilbert spaces

作者:Dymond Michael*
来源:Journal of Mathematical Analysis and Applications, 2014, 413(2): 668-684.
DOI:10.1016/j.jmaa.2013.11.027

摘要

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.

  • 出版日期2014-5-15