On measures simultaneously 2- and 3-invariant (Q1108396)
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scientific article; zbMATH DE number 4067283
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On measures simultaneously 2- and 3-invariant |
scientific article; zbMATH DE number 4067283 |
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On measures simultaneously 2- and 3-invariant (English)
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1988
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H. Furstenberg has conjectured that the only continuous probability measure which is invariant under both \(x\mapsto 2x\) and \(x\mapsto 3x\) mod 1 is the Lebesgue measure. This, in fact is part of a stronger conjecture about continuous S-invariant measures, where S is a nonlacunary semigroup. Under additional mixing conditions this conjecture and related theorems are proven.
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continuous probability measure
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invariant measures
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nonlacunary semigroup
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mixing conditions
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