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Foreword; Preface; Contents; 1 Existence of Finite Invariant Measure; 1.1 Recurrent Transformations; 1.2 Finite Invariant Measure; 2 Transformations with No Finite Invariant Measure; 2.1 Measurable Transformations; 2.2 Ergodic Transformations; 3 Infinite Ergodic Transformations; 3.1 General Properties of Infinite Ergodic Transformations; 3.2 Weakly Wandering Sequences; 3.3 Recurrent Sequences; 3.3.1 Transformations with Recurrent Sequences; 3.3.2 Transformations Without Recurrent Sequences; 4 Three Basic Examples; 4.1 First Basic Example; 4.1.1 Induced Transformations.
6.3 Recurrent Sequences as an Isomorphism Invariant6.3.1 Construction of the Transformation T; 6.3.2 The Recurrent Sequences for T; 6.4 Growth Distributions for a Transformation; 7 Integer Tilings; 7.1 Infinite Tilings of the Integers; 7.1.1 Structure of Complementing Pairs in N; 7.1.2 Complementing Pairs in Z When A or B Is Finite; 7.1.3 Infinite A, B: No Structure Expected; 7.2 How Tilings Arise in Ergodic Theory; 7.2.1 Constructing a Transformation from a Hitting Sequence; 7.3 Examples of Complementing Pairs; 7.3.1 A Complementing Set That Is Not a Hitting Sequence.
7.3.2 A ww Sequence Which Is Not eww for AnyTransformation7.3.3 An eww Sequence with a Complementing Set That Does Not Come from a Point; 7.4 Extending a Finite Set to a Complementing Set; 7.4.1 Definitions and Notations; 7.4.2 Extension Theorem; 7.5 Complementing Sets of A and the 2-Adic Integers; 7.5.1 The 2-Adic Integers; 7.5.2 Condition (iv) Is Not Enough to Be Complementing; 7.6 Examples: Non-isomorphic Transformations; 7.6.1 Two Non-isomorphic Transformations; 7.6.2 An Uncountable Family of Non-isomorphicTransformations; 7.7 An Odometer Construction from M.
7.7.1 Set Theoretic Construction of X7.7.2 Defining the Sequences A and B Associated to M; 7.7.3 The Sequence M and Multiple Recurrence; References; Index.
6.3 Recurrent Sequences as an Isomorphism Invariant6.3.1 Construction of the Transformation T; 6.3.2 The Recurrent Sequences for T; 6.4 Growth Distributions for a Transformation; 7 Integer Tilings; 7.1 Infinite Tilings of the Integers; 7.1.1 Structure of Complementing Pairs in N; 7.1.2 Complementing Pairs in Z When A or B Is Finite; 7.1.3 Infinite A, B: No Structure Expected; 7.2 How Tilings Arise in Ergodic Theory; 7.2.1 Constructing a Transformation from a Hitting Sequence; 7.3 Examples of Complementing Pairs; 7.3.1 A Complementing Set That Is Not a Hitting Sequence.
7.3.2 A ww Sequence Which Is Not eww for AnyTransformation7.3.3 An eww Sequence with a Complementing Set That Does Not Come from a Point; 7.4 Extending a Finite Set to a Complementing Set; 7.4.1 Definitions and Notations; 7.4.2 Extension Theorem; 7.5 Complementing Sets of A and the 2-Adic Integers; 7.5.1 The 2-Adic Integers; 7.5.2 Condition (iv) Is Not Enough to Be Complementing; 7.6 Examples: Non-isomorphic Transformations; 7.6.1 Two Non-isomorphic Transformations; 7.6.2 An Uncountable Family of Non-isomorphicTransformations; 7.7 An Odometer Construction from M.
7.7.1 Set Theoretic Construction of X7.7.2 Defining the Sequences A and B Associated to M; 7.7.3 The Sequence M and Multiple Recurrence; References; Index.