Applications of Point Set Theory in Real Analysis / by A. B. Kharazishvili
(Mathematics and Its Applications ; 429)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
| 出版年 | 1998 |
| 本文言語 | 英語 |
| 大きさ | VIII, 240 p : online resource |
書誌詳細を非表示
| 内容注記 | 0. Introduction: preliminary facts 1. Set-valued mappings 2. Nonmeasurable sets and sets without the Baire property 3. Three aspects of the measure extension problem 4. Some properties of ?-algebras and ?-ideals 5. Nonmeasurable subgroups of the real line 6. Additive properties of invariant ?-ideals on the real line 7. Translations of sets and functions 8. The Steinhaus property of invariant measures 9. Some applications of the property (N) of Luzin 10. The principle of condensation of singularities 11. The uniqueness of Lebesgue and Borel measures 12. Some subsets of spaces equipped with transformation groups 13. Sierpi?ski’s partition and its applications 14. Selectors associated with subgroups of the real line 15. Set theory and ordinary differential equations |
|---|---|
| 一般注記 | This book is devoted to some results from the classical Point Set Theory and their applications to certain problems in mathematical analysis of the real line. Notice that various topics from this theory are presented in several books and surveys. From among the most important works devoted to Point Set Theory, let us first of all mention the excellent book by Oxtoby [83] in which a deep analogy between measure and category is discussed in detail. Further, an interesting general approach to problems concerning measure and category is developed in the well-known monograph by Morgan [79] where a fundamental concept of a category base is introduced and investigated. We also wish to mention that the monograph by Cichon, W«;glorz and the author [19] has recently been published. In that book, certain classes of subsets of the real line are studied and various cardinal valued functions (characteristics) closely connected with those classes are investigated. Obviously, the IT-ideal of all Lebesgue measure zero subsets of the real line and the IT-ideal of all first category subsets of the same line are extensively studied in [19], and several relatively new results concerning this topic are presented. Finally, it is reasonable to notice here that some special sets of points, the so-called singular spaces, are considered in the classi |
| 著者標目 | *Kharazishvili, A. B. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Harmonic analysis LCSH:Measure theory LCSH:Functions of real variables LCSH:Mathematical logic LCSH:Topology FREE:Mathematics FREE:Mathematical Logic and Foundations FREE:Real Functions FREE:Measure and Integration FREE:Topology FREE:Abstract Harmonic Analysis |
| 分 類 | DC23:511.3 |
| 巻冊次 | ISBN:9789401707503 
|
| ISBN | 9789401707503 |
| URL | http://dx.doi.org/10.1007/978-94-017-0750-3 |
目次／あらすじ