Various tools can be used to calculate or estimate the dimension of measures. Using a probabilistic interpretation, we propose very simple proofs for the main inequalities related to this notion. We also discuss the case of quasi-Bernoulli measures and point out the deep link existing between the calculation of the dimension of auxiliary measures and the multifractal analysis.
Yanick Heurteaux. "Dimension of measures: the probabilistic approach." Publ. Mat. 51 (2) 243 - 290, 2007.