A generalization of Marstrand's theorem
  In this paper we prove two general results related to Marstrand's projection theorem in a quite general formulation over separable metric spaces under a suitable transversality hypothesis (the "projections" are in principle only measurable) - the result is flexible enough to, in particular, recover most of the classical Marstrand-like theorems. Our proofs use simpler tools than many classical works in the subject, where some techniques from harmonic analysis or special geometrical structures on the spaces are used. 
Jorge Erick L\'opez, Carlos Gustavo Moreira and Waliston Luiz Silva
math.MG