Infinite Dimensional Multifractal Analysis of the Wiener measure

Abstract

We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called order, for the Wiener measure, which is the probability law of the standard Brownian motion. We also prove the fundamental Frostman Lemma on a large class of Polish spaces, for which the increasing sets lemma holds.