Applications of Point Set Theory in Real Analysis

A.B. Kharazishvili (Autor)

Buch | Softcover

240 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1998
Springer (Verlag)
978-90-481-5006-9 (ISBN)

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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

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.

Erscheint lt. Verlag	6.12.2010
Reihe/Serie	Mathematics and Its Applications ; 429
Zusatzinfo	VIII, 240 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	90-481-5006-X / 904815006X
ISBN-13	978-90-481-5006-9 / 9789048150069
Zustand	Neuware