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The spatially homogeneous Boltzmann equation with hard potentials isconsidered for measure valued initial data having finite mass and energy. Weprove the existence of \emph{weak measure solutions}, with and without angularcutoff on the collision kernel; the proof in particular makes use of anapproximation argument based on the Mehler transform. Moment productionestimates in the usual form and in the exponential form are obtained for thesesolutions. Finally for the Grad angular cutoff, we also establish uniquenessand strong stability estimate on these solutions.

On Measure Solutions of the Boltzmann Equation, part I: Moment Production and Stability Estimates