Author | Srivastava, S. M. author |
---|---|
Title | A Course on Borel Sets [electronic resource] / by S. M. Srivastava |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1998 |
Connect to | http://dx.doi.org/10.1007/978-3-642-85473-6 |
Descript | online resource |
1 Cardinal and Ordinal Numbers -- 1.1 Countable Sets -- 1.2 Order of Infinity -- 1.3 The Axiom of Choice -- 1.4 More on Equinumerosity -- 1.5 Arithmetic of Cardinal Numbers -- 1.6 Well-Ordered Sets -- 1.7 Transfinite Induction -- 1.8 Ordinal Numbers -- 1.9 Alephs -- 1.10 Trees -- 1.11 Induction on Trees -- 1.12 The Souslin Operation -- 1.13 Idempotence of the Souslin Operation -- 2 Topological Preliminaries -- 2.1 Metric Spaces -- 2.2 Polish Spaces -- 2.3 Compact Metric Spaces -- 2.4 More Examples -- 2.5 The Baire Category Theorem -- 2.6 Transfer Theorems -- 3 Standard Borel Spaces -- 3.1 Measurable Sets and Functions -- 3.2 Borel-Generated Topologies -- 3.3 The Borel Isomorphism Theorem -- 3.4 Measures -- 3.5 Category -- 3.6 Borel Pointclasses -- 4 Analytic and Coanalytic Sets -- 4.1 Projective Sets -- 4.2 ?11 and ?11 Complete Sets -- 4.3 Regularity Properties -- 4.4 The First Separation Theorem -- 4.5 One-to-One Borel Functions -- 4.6 The Generalized First Separation Theorem -- 4.7 Borel Sets with Compact Sections -- 4.8 Polish Groups -- 4.9 Reduction Theorems -- 4.10 Choquet Capacitability Theorem -- 4.11 The Second Separation Theorem -- 4.12 Countable-to-One Borel Functions -- 5 Selection and Uniformization Theorems -- 5.1 Preliminaries -- 5.2 Kuratowski and Ryll-Nardzewskiโs Theorem -- 5.3 Dubins โ Savage Selection Theorems -- 5.4 Partitions into Closed Sets -- 5.5 Von Neumannโs Theorem -- 5.6 A Selection Theorem for Group Actions -- 5.7 Borel Sets with Small Sections -- 5.8 Borel Sets with Large Sections -- 5.9 Partitions into G? Sets -- 5.10 Reflection Phenomenon -- 5.11 Complementation in Borel Structures -- 5.12 Borel Sets with ?-Compact Sections -- 5.13 Topological Vaught Conjecture -- 5.14 Uniformizing Coanalytic Sets -- References