Infinite convolutions of probability measures on Polish semigroups

Kouji Yano

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arXiv · 2108.12588

Infinite convolutions of probability measures on Polish semigroups

Kouji Yano

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Abstract

This expository paper is intended for a short self-contained introduction to the theory of infinite convolutions of probability measures on Polish semigroups. We give the proofs of the Rees decomposition theorem of completely simple semigroups, the Ellis--\.{Z}elazko theorem, the convolution factorization theorem of convolution idempotents, and the convolution factorization theorem of cluster points of infinite convolutions.

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Kouji Yano. 2021-08-28. Infinite convolutions of probability measures on Polish semigroups. https://arxiv.org/abs/2108.12588

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