Abstract
This is a survey on geometric constructions in multifractal analysis of measures. We show that the multifractal formalism introduced by Olsen [Ol11] and Peyriere [Pey] leads to a multifractal geometry for product measures, for slices of measures (i.e. intersections of measures with lower dimensional subspaces), and for general intersections of measures, which is analogous to the fractal geometry for product sets, for slices of sets (i.e. intersections of sets with lower dimensional subspaces), and for general intersections of sets, respectively.
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