Preface Chapter 1. Lebesgue Measure in Euclidean Space 1. An Introduction to Lebesgue Measure 2. The Brunn-Minkowski Theorem 3. Covering Theorem of Vitali 4. Notes and Remarks Chapter 2. Measures on Metric Spaces 1. Generalities on Outer Measures 2. Regularity 3. Invariant Measures on Rr 4. Notes and Remarks Chapter 3. Introduction to Topological Groups 1. Introduction 2. The Classical (Locally Compact) Groups 3. The Birkhoff-Kakutani Theorem 4. Products of Topological Spaces 5. Notes and Remarks Chapter 4. Banach and Measure 1. Banach Limits 2. Banach and Haar Measure 3. Saks' Proof of C(Q)*,Q a Compact Metric Space 4. The Lebesgue Integral on Abstract Spaces 5. Notes and Remarks Chapter 5. Compact Groups Have a Haar Measure 1. The Arzel?-Ascoli Theorem 2. Existence and Uniqueness of an Invariant Mean 3. The Dual of C(K) 4. Notes and Remarks Chapter 6. Applications 1. Homogeneous Spaces 2. Unitary Representations:The Peter-Weyl Theorem 3. Pietsch Measures 4. Notes and Remarks Chapter 7. Haar Measure on Locally Compact Groups 1. Positive Linear Functionals 2. Weil's Proof of Existence 3. A Remarkable Approximation Theorem of Henri Cartan 4. Cartan's Proof of Existence of a Left Haar Integral 5. Cartan's Proof of Uniqueness 6. Notes and Remarks Chapter 8. Metric Invariance and Haar Measure 1. Notes and Remarks Chapter 9. Steinlage on Haar Measure 1. Uniform Spaces: The Basics 2. Some Miscellaneous Facts and Features about Uniform Spaces 3. Compactness in Uniform Spaces 4. From Contents to Outer Measures 5. Existence of G-invariant Contents 6. Steinlage: Uniqueness and Weak Transitivity 7. Notes and Remarks
Chapter 10. Oxtoby's View of Haar Measure 1. Invariant Measures on Polish Groups 2. Notes and Remarks Appendix A Appendix B Bibliography Author Index Subject Index
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