31 pagesLet (T,d) be the random real tree with root ρ coded by a Brownian excursion. So (T,d) is (up to normalisation) Aldous CRT \cite{AldousI} (see Le Gall \cite{LG91}). The a-level set of T is the set T(a) of all points in T that are at distance a from the root. We know from Duquesne and Le Gall \cite{DuLG06} that for any fixed a∈(0,∞), the measure ℓa that is induced on T(a) by the local time at a of the Brownian excursion, is equal, up to a multiplicative constant, to the Hausdorff measure in T with gauge function g(r)=rloglog1/r, restricted to T(a). As suggested by a result due to Perkins \cite{Per88,Per89} for super-Brownian motion, we prove in this paper a more precise statement that holds almost surely uniformly in a, and we specify the multiplicative constant. Namely, we prove that almost surely for any a∈(0,∞), ℓa(⋅)=21Hg(⋅∩T(a)), where Hg stands for the g-Hausdorff measure
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