Absolutely continuous, invariant measures for dissipative, ergodic transformations

Jon Aaronson; Tom Meyerovitch

doi:10.4064/cm110-1-7

Absolutely continuous, invariant measures for dissipative, ergodic transformations

Jon Aaronson, Tom Meyerovitch

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

4 Scopus citations

Abstract

We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.

Original language	English
Pages (from-to)	193-199
Number of pages	7
Journal	Colloquium Mathematicum
Volume	110
Issue number	1
DOIs	https://doi.org/10.4064/cm110-1-7
State	Published - 1 Jan 2008
Externally published	Yes

Keywords

Dissipative
Ergodic
Exact
Measure preserving transformation
Wandering set

ASJC Scopus subject areas

Mathematics (all)

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10.4064/cm110-1-7

Cite this

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abstract = "We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.",

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AU - Meyerovitch, Tom

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N2 - We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.

AB - We show that a dissipative, ergodic measure preserving transformation of a σ-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.

KW - Dissipative

KW - Ergodic

KW - Exact

KW - Measure preserving transformation

KW - Wandering set

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Absolutely continuous, invariant measures for dissipative, ergodic transformations

Abstract

Keywords

ASJC Scopus subject areas

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