On measures simultaneously 2- and 3-invariant

@article{Lyons1988OnMS,
  title={On measures simultaneously 2- and 3-invariant},
  author={R. Lyons},
  journal={Israel Journal of Mathematics},
  year={1988},
  volume={61},
  pages={219-224}
}
  • R. Lyons
  • Published 1988
  • Mathematics
  • 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. 
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    References

    SHOWING 1-6 OF 6 REFERENCES
    On normal numbers
    • 10
    • PDF
    On the representation of an integer in two different bases.
    • 65
    Mixing and asymptotic distribution modulo 1
    • 6
    • Highly Influential
    • PDF
    On normal numbers.
    • 92
    • PDF
    PV-numbers and sets of multiplicity
    • 40
    Riesz Products and Normal Numbers
    • 18