On some notions of tangent space to a measure

We consider some definitions of tangent space to a Radon measure mu on R-n that have been given in the literature. In particular, we focus our attenti on on a recent distributional notion of tangent Vector field to a measure a nd 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.