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 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.

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

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.

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

scholarly journals On rationally ergodic and rationally weakly mixing rank-one transformations

2014 ◽  
Vol 35 (4) ◽  
pp. 1141-1164 ◽  
Author(s):  
IRVING DAI ◽  
XAVIER GARCIA ◽  
TUDOR PĂDURARIU ◽  
CESAR E. SILVA
Keyword(s):  
Weak Mixing ◽  
Infinite Measure ◽  
Markov Shifts ◽  
Rank One ◽  
Measure Spaces ◽  
Metric Invariant ◽  
Weakly Mixing

AbstractWe study the notions of weak rational ergodicity and rational weak mixing as defined by J. Aaronson [Rational ergodicity and a metric invariant for Markov shifts.Israel J. Math. 27(2) (1977), 93–123; Rational weak mixing in infinite measure spaces.Ergod. Th. & Dynam. Sys.2012, to appear.http://arxiv.org/abs/1105.3541]. We prove that various families of infinite measure-preserving rank-one transformations possess or do not posses these properties, and consider their relation to other notions of mixing in infinite measure.

On category of mixing in infinite measure spaces

1971 ◽  
Vol 5 (4) ◽  
pp. 319-330 ◽  
Author(s):  
Usha Sachdeva
Keyword(s):  
Infinite Measure ◽  
Measure Spaces

On the entropy of a product endomorphism in infinite measure spaces

1969 ◽  
Vol 12 (4) ◽  
pp. 290-292 ◽  
Author(s):  
Eugene M. Klimko
Keyword(s):  
Infinite Measure ◽  
Measure Spaces
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