Israel Journal of Mathematics

, Volume 61, Issue 2, pp 219–224 | Cite as

On measures simultaneously 2- and 3-invariant

  • Russell Lyons
Article

Abstract

Furstenberg has conjectured that the only continuous probability measure on the circleT=R/Z which is invariant under bothx ↦ 2x andx ↦ 3x is Lebesgue measure. We shall show that under additional hypotheses, this is true. We also discuss related conjectures and theorems.

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Copyright information

© The Weizmann Sciene Press of Israel 1988

Authors and Affiliations

  • Russell Lyons
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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