Inserted: 15 mar 1998
Last Updated: 3 jun 2013
Journal: Proc. Royal Soc. Edinburgh
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.