Manuscripta Mathematica

, Volume 142, Issue 3–4, pp 475–489

# Density rate of a set, application to rectifiability results for measurable jets

Article

## Abstract

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 Classifications

28A75 26A24 49Q15

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