A Course on Borel SetsSpringer Science & Business Media, 13 apr 1998 - 264 pagine A Course on Borel sets provides a thorough introduction to Borel sets and measurable selections and acts as a stepping stone to descriptive set theory by presenting important techniques such as universal sets, prewellordering, scales, etc. It is well suited for graduate students exploring areas of mathematics for their research and for mathematicians requiring Borel sets and measurable selections in their work. It contains significant applications to other branches of mathematics and can serve as a self- contained reference accessible by mathematicians in many different disciplines. It is written in an easily understandable style and employs only naive set theory, general topology, analysis, and algebra. A large number of interesting exercises are given throughout the text. |
Sommario
Cardinal and Ordinal Numbers | 1 |
Topological Preliminaries | 39 |
Standard Borel Spaces 81 | 80 |
Analytic and Coanalytic Sets | 127 |
Selection and Uniformization Theorems | 183 |
| 241 | |
Glossary 251 | 250 |
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Parole e frasi comuni
A-measurable admits a Borel algebra analytic sets analytic subsets assume Baire Baire category theorem Baire property bijection Borel isomorphism Borel map Borel measurable Borel set Borel subset called Cantor cardinality cl(U Clearly closed set closed subset closed under countable coanalytic comeager completely metrizable continuous map convergent Corollary countable base countable unions defined denote dense element equivalence classes equivalence relation Example Exercise f is continuous finite function f Gs set Hence homeomorphic induction infinite Lebesgue lemma Let f Let G lim sup Lo-measurable map f meager measurable space nonmeager Note o-algebra one-to-one open set ordinal numbers pairwise disjoint pointclass Polish group Polish space Polish topology Proposition prove real numbers result follows second countable separable sequence Souslin operation Suppose Take topological space uncountable Polish space w₁ well-ordered set zero-dimensional Zorn's lemma π₁ πχ ω₁
Brani popolari
Pagina 244 - Kechris and A. Louveau, Descriptive Set Theory and the Structure of Sets of Uniqueness, London Math. Soc. Lecture Note Ser., 128, Cambridge Univ.