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

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.