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AbstractBrownian multiplicative chaos measures, introduced in Jego (Ann Probab 48:1597–1643, 2020), Aïdékon et al. (Ann Probab 48(4):1785–1825, 2020) and Bass et al. (Ann Probab 22:566–625, 1994), are random Borel measures that can be formally defined by exponentiating $$\gamma $$ γ times the square root of the local times of planar Brownian motion. So far, only the subcritical measures where the parameter $$\gamma $$ γ is less than 2 were studied. This article considers the critical case wheredoi:10.1007/s00440-021-01051-7 fatcat:eqwqykhmwvfbhbvks6pi54lxr4