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Measurable quotients of unipotent translations on homogeneous spaces


Author: Dave Witte
Journal: Trans. Amer. Math. Soc. 345 (1994), 577-594
MSC: Primary 22D40; Secondary 28C10, 28D15, 58F11
DOI: https://doi.org/10.1090/S0002-9947-1994-1181187-4
Correction: Trans. Amer. Math. Soc. 349 (1997), 4685-4688.
MathSciNet review: 1181187
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Abstract: Let U be a nilpotent, unipotent subgroup of a Lie group G, and let $ \Gamma $ be a closed subgroup of G. Marina Ratner showed that every ergodic U-invariant probability measure on the homogeneous space $ \Gamma \backslash G$ is of a simple algebraic form. We use this fundamental new result to show that every measurable quotient of the U-action on $ \Gamma \backslash G$ is of a simple algebraic form. Roughly speaking, any quotient is a double-coset space $ \Lambda \backslash G/K$.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1181187-4
Article copyright: © Copyright 1994 American Mathematical Society

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