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The volume measure of the Brownian sphere is a Hausdorff measure (2105.05615v3)
Published 12 May 2021 in math.PR
Abstract: We prove that the volume measure of the Brownian sphere is equal to a constant multiple of the Hausdorff measure associated with the gauge function $h(r)=r4\log\log(1/r)$. This shows in particular that the volume measure of the Brownian sphere is determined by its metric structure. As a key ingredient of our proofs, we derive precise estimates on moments of the volume of balls in the Brownian sphere.
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