{
  "id": "2108.12588",
  "version": "v1",
  "published": "2021-08-28T07:15:06.000Z",
  "updated": "2021-08-28T07:15:06.000Z",
  "title": "Infinite convolutions of probability measures on Polish semigroups",
  "authors": [
    "Kouji Yano"
  ],
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-28T07:15:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite convolutions",
      "probability measures",
      "polish semigroups",
      "convolution factorization theorem",
      "rees decomposition theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}