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

General Mathematics

Access to Document

10.4064/cm110-1-7

Cite this

@article{655d9b5764744aff941a8f228e44d357,

title = "Absolutely continuous, invariant measures for dissipative, ergodic transformations",

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.",

keywords = "Dissipative, Ergodic, Exact, Measure preserving transformation, Wandering set",

author = "Jon Aaronson and Tom Meyerovitch",

note = "Publisher Copyright: {\textcopyright} Instytut Matematyczny PAN, 2008.",

year = "2008",

month = jan,

day = "1",

doi = "10.4064/cm110-1-7",

language = "English",

volume = "110",

pages = "193--199",

journal = "Colloquium Mathematicum",

issn = "0010-1354",

publisher = "Institute of Mathematics. Polish Academy of Sciences",

number = "1",

}

TY - JOUR

T1 - Absolutely continuous, invariant measures for dissipative, ergodic transformations

AU - Aaronson, Jon

AU - Meyerovitch, Tom

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2008.

PY - 2008/1/1

Y1 - 2008/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=84876059752&partnerID=8YFLogxK

U2 - 10.4064/cm110-1-7

DO - 10.4064/cm110-1-7

M3 - Article

AN - SCOPUS:84876059752

SN - 0010-1354

VL - 110

SP - 193

EP - 199

JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

IS - 1

ER -

Absolutely continuous, invariant measures for dissipative, ergodic transformations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this