On measures simultaneously 2- and 3-invariant

  title={On measures simultaneously 2- and 3-invariant},
  author={R. Lyons},
  journal={Israel Journal of Mathematics},
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.