Calculus of Variations and Geometric Measure Theory

I. FragalĂ  - C. Mantegazza

On some Notions of Tangent Space to a Measure

created on 15 Mar 1998
modified by root on 03 Jun 2013


Published Paper

Inserted: 15 mar 1998
Last Updated: 3 jun 2013

Journal: Proc. Royal Soc. Edinburgh
Volume: 129A
Pages: 331-342
Year: 1999


We consider some definitions of tangent space to a Radon measure on Rn which have been given in the literature. In particular we focus our attention on a recent distributional notion of tangent vector field to a measure and we compare it to other definitions coming from Geometric Measure Theory, based on the idea of blow-up. After showing some classes of examples, we prove an estimate from above for the dimension of the tangent spaces and a rectifiability theorem which also includes the case of measures supported on sets of variable dimension.