On the ergodic theory of non-integrable functions and infinite measure spaces

1977 ◽  
Vol 27 (2) ◽  
pp. 163-173 ◽  
Author(s):  
Jon Aaronson
Keyword(s):  
Ergodic Theory ◽  
Infinite Measure ◽  
Integrable Functions ◽  
Measure Spaces

Poincaré sequences in infinite measure spaces and complementing subsets of the integers

1988 ◽  
pp. 154-157 ◽  
Author(s):  
Stanley Eigen ◽  
Arshag Hajian
Keyword(s):  
Infinite Measure ◽  
Measure Spaces

scholarly journals LIMIT LAWS FOR DISTORTED CRITICAL RETURN TIME PROCESSES IN INFINITE ERGODIC THEORY

2007 ◽  
Vol 07 (01) ◽  
pp. 103-121 ◽  
Author(s):  
MARC KESSEBÖHMER ◽  
MEHDI SLASSI
Keyword(s):  
Asymptotic Behaviour ◽  
Uniform Distribution ◽  
Ergodic Theory ◽  
Ergodic Measure ◽  
Return Time ◽  
Limit Laws ◽  
Measure Spaces ◽  
Distribution Laws ◽  
Infinite Ergodic Theory ◽  
Measure Preserving Transformations

We consider conservative ergodic measure preserving transformations on infinite measure spaces and investigate the asymptotic behaviour of distorted return time processes with respect to sets satisfying a type of Darling–Kac condition. We identify two critical cases for which we prove uniform distribution laws.

scholarly journals On mixing in infinite measure spaces

1968 ◽  
Vol 74 (6) ◽  
pp. 1150-1156 ◽  
Author(s):  
U. Krengel ◽  
L. Sucheston
Keyword(s):  
Infinite Measure ◽  
Measure Spaces

scholarly journals Slow entropy and differentiable models for infinite-measure preserving ℤk actions

2012 ◽  
Vol 32 (2) ◽  
pp. 653-674 ◽  
Author(s):  
MICHAEL HOCHMAN
Keyword(s):  
Compact Manifold ◽  
Borel Measure ◽  
Infinite Measure ◽  
Group Of Diffeomorphisms ◽  
Measure Spaces

AbstractWe define ‘slow’ entropy invariants for ℤd actions on infinite measure spaces, which measure growth of itineraries at subexponential scales. We use this notion to construct infinite-measure preserving ℤ2 actions which cannot be realized as a group of diffeomorphisms of a compact manifold preserving a Borel measure, in contrast to the situation for ℤ actions, where every infinite-measure preserving action can be realized in this way.

scholarly journals Symmetric Birkhoff sums in infinite ergodic theory

2016 ◽  
Vol 37 (8) ◽  
pp. 2394-2416 ◽  
Author(s):  
JON AARONSON ◽  
ZEMER KOSLOFF ◽  
BENJAMIN WEISS
Keyword(s):  
Ergodic Theory ◽  
Recurrent Events ◽  
Integrable Functions ◽  
Infinite Ergodic Theory

We show that the absolutely normalized, symmetric Birkhoff sums of positive integrable functions in infinite, ergodic systems never converge pointwise even though they may be almost surely bounded away from zero and infinity. Also, we consider the latter phenomenon and characterize it among transformations admitting generalized recurrent events.

A new characterization of the Haagerup property by actions on infinite measure spaces

2020 ◽  
pp. 1-20
Author(s):  
THIEBOUT DELABIE ◽  
PAUL JOLISSAINT ◽  
ALEXANDRE ZUMBRUNNEN
Keyword(s):  
Finite Measure ◽  
Invariant Mean ◽  
Locally Compact ◽  
Haagerup Property ◽  
Infinite Measure ◽  
Measurable Functions ◽  
Measure Spaces ◽  
Definition Of

The aim of the article is to provide a characterization of the Haagerup property for locally compact, second countable groups in terms of actions on $\unicode[STIX]{x1D70E}$ -finite measure spaces. It is inspired by the very first definition of amenability, namely the existence of an invariant mean on the algebra of essentially bounded, measurable functions on the group.

The Converse of the Dominated Ergodic Theorem in Hurewicz Setting

1991 ◽  
Vol 34 (3) ◽  
pp. 405-411
Author(s):  
László I. Szabó
Keyword(s):  
Ergodic Theorem ◽  
Orlicz Spaces ◽  
Maximal Inequality ◽  
Infinite Measure ◽  
Measure Spaces

AbstractThe converse of the dominated ergodic theorem in infinite measure spaces is extended to non-singular transformations, i.e. transformations that only preserve the measure of null sets. An inverse weak maximal inequality is given and then applied to obtain related results in Orlicz spaces.

Conjugates of Infinite Measure Preserving Transformations

1988 ◽  
Vol 40 (3) ◽  
pp. 742-749
Author(s):  
S. Alpern ◽  
J. R. Choksi ◽  
V. S. Prasad
Keyword(s):  
Conjugacy Class ◽  
Ergodic Theory ◽  
Lebesgue Space ◽  
Finite Measure ◽  
Infinite Measure ◽  
Ergodic Automorphism ◽  
Measurable Set ◽  
Image Position ◽  
Measure Preserving Transformations

In this paper we consider a question concerning the conjugacy class of an arbitrary ergodic automorphism σ of a sigma finite Lebesgue space (X, , μ) (i.e., a is a ju-preserving bimeasurable bijection of (X, , μ). Specifically we proveTHEOREM 1. Let τ, σ be any pair of ergodic automorphisms of an infinite sigma finite Lebesgue space (X, , μ). Let F be any measurable set such thatThen there is some conjugate σ' of σ such that σ'(x) = τ(x) for μ-almost every x in F.The requirement that F ∪ τF has a complement of infinite measure is, for example, satisfied when F has finite measure, and in that case, the theorem was proved by Choksi and Kakutani ([7], Theorem 6).Conjugacy theorems of this nature have proved to be very useful in proving approximation results in ergodic theory. These conjugacy results all assert the denseness of the conjugacy class of an ergodic (or antiperiodic) automorphism in various topologies and subspaces.

scholarly journals On decomposition of transformations in infinite measure spaces

1973 ◽  
Vol 44 (2) ◽  
pp. 733-738 ◽  
Author(s):  
Ryōtarō Satō
Keyword(s):  
Infinite Measure ◽  
Measure Spaces ◽  
Decomposition Of Transformations
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