Epimorphic subgroups and invariant measures

Shahar Mozes

doi:10.1017/S0143385700009871

Epimorphic subgroups and invariant measures

Shahar Mozes^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

It is shown that a probability measure on a homogeneous space Γ\G which is invariant under a subgroup H < G which is epimorphic in a subgroup L < G is invariant under L. When L = G we obtain a subgroup H such that for any lattice Γ < G its action on Γ\G is uniquely ergodic.

Original language	English
Pages (from-to)	1207-1210
Number of pages	4
Journal	Ergodic Theory and Dynamical Systems
Volume	15
Issue number	6
DOIs	https://doi.org/10.1017/S0143385700009871
State	Published - Dec 1995

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title = "Epimorphic subgroups and invariant measures",

abstract = "It is shown that a probability measure on a homogeneous space Γ\textbackslash{}G which is invariant under a subgroup H < G which is epimorphic in a subgroup L < G is invariant under L. When L = G we obtain a subgroup H such that for any lattice Γ < G its action on Γ\textbackslash{}G is uniquely ergodic.",

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AB - It is shown that a probability measure on a homogeneous space Γ\G which is invariant under a subgroup H < G which is epimorphic in a subgroup L < G is invariant under L. When L = G we obtain a subgroup H such that for any lattice Γ < G its action on Γ\G is uniquely ergodic.

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JO - Ergodic Theory and Dynamical Systems

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Epimorphic subgroups and invariant measures

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