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The γ-stable trees are random measured compact metric spaces that appear as the scaling limit of Galton-Watson trees whose offspring distribution lies in a γ-stable domain, γ ∈ (1, 2]. They form a specific class of Lévy trees (introduced by Le Gall and Le Jan in  ) and the Brownian case γ = 2 corresponds to Aldous Continuum Random Tree (CRT). In this paper, we study fine properties of the mass measure, that is the natural measure on γ-stable trees. We first discuss the minimum of the massdoi:10.24033/bsmf.2664 fatcat:a6caxisukvcsjo2cev5q4dj5ly