Weakly Wandering Sequences in Ergodic Theory
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.
Provides a full account of the problem of finite invariant measures for measurable transformations with a detailed explanation of its historyExplains in detail the properties and significance of weakly wandering and other sequences of integers attached to infinite ergodic transformationsShows interesting new connections between ergodic theory and certain number theoretic problems