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 . This shows in particular that the volume measure of the Brownian sphere is determined by its metric structure.
Funding Statement
Supported by the ERC Advanced Grant 740943 GeoBrown.
Acknowledgments
I thank two anonymous referees for several useful remarks on the first version of this work.
Citation
Jean-François Le Gall. "The volume measure of the Brownian sphere is a Hausdorff measure." Electron. J. Probab. 27 1 - 28, 2022. https://doi.org/10.1214/22-EJP837
Information
