Preprint
(2010)
Author:
Silvano Delladio
Abstract:
Given m > 0 and a measurable set E Ì Rn, E(m) denotes the set of m-density points of E, namely the points x in Rn at which Ln(B(x,r)\E) is an infinitesimal of order greater than rm (as r goes to 0). We investigate the size of E(m) in the particular case when E is a generalized Cantor set in R. Moreover we prove the following result. Let j be in Ch(W) and F be in Ch(W;Rn)), where W is an open subset of Rn and h ³ 1. If K: = { x Î W | Ñj(x) = F(x)} then the graph of j|WÇK(n+h) is a n-dimensional Ch+1-rectifiable set.
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[BibTeX Entry]
Available Files:
abstract.tex (abstract.ps, abstract.pdf)
