Weakly Wandering Sequences in Ergodic Theory

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Springer, Aug 19, 2014 - Mathematics - 153 pages

The appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure.

This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure. Connections of these sequences to additive number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory is adequate for the reader.

 

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Contents

1 Existence of Finite Invariant Measure
1
2 Transformations with No Finite Invariant Measure
17
3 Infinite Ergodic Transformations
25
4 Three Basic Examples
41
5 Properties of Various Sequences
64
6 Isomorphism Invariants
79
7 Integer Tilings
103
References
147
Index
150
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About the author (2014)

Arshag Hajian Professor of Mathematics at Northeastern University, Boston, Massachusetts, U.S.A. Stanley Eigen Professor of Mathematics at Northeastern University, Boston, Massachusetts, U. S. A. Raj. Prasad Professor of Mathematics at University of Massachusetts at Lowell, Lowell, Massachusetts, U.S.A. Yuji Ito Professor Emeritus of Keio University, Yokohama, Japan.

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