No distribution is prime

I. Z. Ruzsa, G. J. Székely

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let ℱ denote the convolution semigroup of probability distributions on the real line. We prove that no element of ℱ is prime in the sense that given an ℱ one can always find two distributions G,H∈ℱ such that F is a convolution factor of G*H but neither of G nor of H. In contrast, ℱ is known to possess many irreducible elements.

Original languageEnglish
Pages (from-to)263-269
Number of pages7
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume70
Issue number2
DOIs
Publication statusPublished - Aug 1 1985

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Mathematics(all)

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