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Jacques Peyrière

Université Paris-Sud (France)

On the multifractal formalism

An early mathematical treatment of the multifractal analysis of measures appeared in a joint article with G. Brown and G. Michon in 1992. An account of further developments is given: the Olsen formalism, the last version of its justification and some extension. In particular, this allows to extend the Besicovitch theorem on linear sets defined in terms of upper frequency of digits in base 2 expansions to an arbitrary base.