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Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution

Wojciech Młotkowski, Noriyoshi Sakuma (2011)

Banach Center Publications

We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then ( μ μ ) s = μ s μ s and if ν₁,ν₂ are symmetric then ( ν ν ) ( 2 ) = ν ( 2 ) ν ( 2 ) . Finally we investigate necessary and sufficient conditions under which the latter equality holds.

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