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arXiv · 2512.06984

Infinite Dimensional Multifractal Analysis of the Wiener measure

Aihua Fan·Mathieu Helfter
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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.

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Aihua Fan, Mathieu Helfter. 2025-12-07. Infinite Dimensional Multifractal Analysis of the Wiener measure. https://arxiv.org/abs/2512.06984

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