Density rate of a set, application to rectifiability results for measurable jets
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In this work, we present some new results concerning the sets of h-density points and their application in the context of the Whitney extension theorem. In particular, we establish a simple relation between the amount of density of a set E at x and the property that u φ E has derivative of order h at x in the L p sense whenever u is continuous at x. Moreover we prove Whitney-type rectifiability results for measurable jets restricted to sets of high density points in its domain. It’s worth mentioning the case when the domain is a locally finite perimeter set.
Mathematics Subject Classifications28A75 26A24 49Q15
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- 3.Bojarski, B.: Differentiation of measurable functions and Whitney-Luzin type structure theorems. Helsinki University of Technology Institute of Mathematics Research Reports A572. http://math.tkk.fi/reports/a572.pdf
- 6.Delladio, S.: Dilatations of graphs and Taylor’s formula: some results about convergence. Real Anal. Exch. 29(2), 687–713 (2003/2004)Google Scholar
- 9.Delladio, S.: A Whitney-type result about rectifiability of graphs. Preprint (2013)Google Scholar
- 10.Evans, C.L., Gariepy, F.R.: Lecture notes on measure theory and fine properties of functions. (Studies in Advanced Mathematics) CRC Press, New York (1992)Google Scholar
- 14.Ziemer, W.P.: Weakly differentiable functions. GTM 120, Springer, Berlin (1989)Google Scholar