Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution
Volume 96 / 2011
Banach Center Publications 96 (2011), 271-276
MSC: 46L53, 60E10.
DOI: 10.4064/bc96-0-18
Abstract
We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if $\mu_1,\mu_2$ are probability measures on $[0,\infty)$ then $\left(\mu_1\uplus\mu_2\right)^{\mathbf{s}} =\mu_1^{\mathbf{s}}\uplus\mu_2^{\mathbf{s}}$ and if $\nu_1,\nu_2$ are symmetric then $\left(\nu_1\uplus\nu_2\right)^{(2)} =\nu_1^{(2)}\uplus\nu_2^{(2)}$. Finally we investigate necessary and sufficient conditions under which the latter equality holds.
