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

Péter Móra, K. 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 2009

Fingerprint

Random Sets
Cantor set
Lebesgue Measure
Difference Set
Interval
Line
Sufficient Conditions
Family

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Lebesgue measure of the algebraic difference of two random Cantor sets. / Móra, Péter; Simon, K.; Solomyak, Boris.

In: Indagationes Mathematicae, Vol. 20, No. 1, 03.2009, p. 131-149.

Research output: Contribution to journalArticle

Móra, Péter ; Simon, K. ; Solomyak, Boris. / The Lebesgue measure of the algebraic difference of two random Cantor sets. In: Indagationes Mathematicae. 2009 ; Vol. 20, No. 1. pp. 131-149.
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