Area formula for centered Hausdorff measures in metric spaces

Motivated by an example in Magnani (in press), we study, inside a separable metric space (X,d)(X,d), the relations between centered and non centered mm-dimensional densities of a Radon measure μμ in XX and their relations with spherical and centered spherical mm-dimensional Hausdorff measures. Eventually we give an application to finite perimeter sets in Carnot groups.