No distribution is prime

I. Z. Ruzsa, G. J. Székely

Research output: Contribution to journalArticle

3 Citations (Scopus)


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
Issue number2
Publication statusPublished - Aug 1 1985

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Mathematics(all)

Fingerprint Dive into the research topics of 'No distribution is prime'. Together they form a unique fingerprint.

  • Cite this