The Lebesgue measure of the algebraic difference of two random Cantor sets

Péter Móra, Károly Simon, Boris Solomyak

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper we consider a family of random Cantor sets on the line. We give some sufficient conditions when the Lebesgue measure of the arithmetic difference is positive. Combining this with the main result of a recent joint paper of the second author with M. Dekking we construct random Cantor sets F1, F2 such that the arithmetic difference set F2 - F1 does not contain any intervals but ℒeb(F2 - F1)> 0 almost surely, conditioned on non-extinction.

Original languageEnglish
Pages (from-to)131-149
Number of pages19
JournalIndagationes Mathematicae
Volume20
Issue number1
DOIs
Publication statusPublished - Mar 1 2009

    Fingerprint

Keywords

  • Branching processes with random environment
  • Difference of Cantor sets
  • Palis conjecture
  • Random fractals

ASJC Scopus subject areas

  • Mathematics(all)

Cite this