Nonmeasurable sets and functions (Record no. 21908)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 05699cam a2200697Ia 4500 |
| 001 - CONTROL NUMBER | |
| control field | ocn162130131 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20141103172227.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cn||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 070802s2004 ne ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | |
| Language of cataloging | eng |
| Transcribing agency | OPELS |
| Modifying agency | OCLCQ |
| -- | OPELS |
| -- | OCLCQ |
| -- | N$T |
| -- | MERUC |
| -- | E7B |
| -- | IDEBK |
| -- | DEBBG |
| -- | TULIB |
| -- | OCLCO |
| -- | OCLCQ |
| -- | OPELS |
| -- | OCLCF |
| 019 ## - | |
| -- | 62386973 |
| -- | 441789250 |
| -- | 648257746 |
| -- | 779920177 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780444516268 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0444516263 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1423741846 (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781423741848 (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0080479766 (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780080479767 (electronic bk.) |
| 029 1# - (OCLC) | |
| OCLC library identifier | NZ1 |
| System control number | 12434419 |
| 029 1# - (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000048130622 |
| 029 1# - (OCLC) | |
| OCLC library identifier | DEBBG |
| System control number | BV039830096 |
| 029 1# - (OCLC) | |
| OCLC library identifier | NZ1 |
| System control number | 15292832 |
| 029 1# - (OCLC) | |
| OCLC library identifier | DEBBG |
| System control number | BV036962227 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)162130131 |
| Canceled/invalid control number | (OCoLC)62386973 |
| -- | (OCoLC)441789250 |
| -- | (OCoLC)648257746 |
| -- | (OCoLC)779920177 |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 107953:107995 |
| Source of stock number/acquisition | Elsevier Science & Technology |
| Note | http://www.sciencedirect.com |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA312 |
| Item number | .K526 2004eb |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | QA |
| Source | lcco |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 005000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 034000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.42 |
| Edition number | 22 |
| 049 ## - LOCAL HOLDINGS (OCLC) | |
| Holding library | TEFA |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Kharazishvili, A. B. |
| 245 10 - TITLE STATEMENT | |
| Title | Nonmeasurable sets and functions |
| Medium | [electronic resource] / |
| Statement of responsibility, etc. | A.B. Kharazishvili. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc. | Amsterdam ; |
| -- | Boston : |
| Name of publisher, distributor, etc. | Elsevier, |
| Date of publication, distribution, etc. | 2004. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xi, 337 p.) |
| 490 1# - SERIES STATEMENT | |
| Series statement | North-Holland mathematics studies, |
| International Standard Serial Number | 0304-0208 ; |
| Volume/sequential designation | 195 |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics: 1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces; 2. The theory of non-real-valued-measurable cardinals; 3. The theory of invariant (quasi-invariant) extensions of invariant (quasi-invariant) measures. These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions. highlights the importance of nonmeasurable sets (functions) for general measure extension problem. Deep connections of the topic with set theory, real analysis, infinite combinatorics, group theory and geometry of Euclidean spaces shown and underlined. self-contained and accessible for a wide audience of potential readers. Each chapter ends with exercises which provide valuable additional information about nonmeasurable sets and functions. Numerous open problems and questions. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Contents -- Preface. -- 1. The Vitali theorem. -- 2. The Bernstein construction. -- 3. Nonmeasurable sets associated with Hamel bases. -- 4. The Fubini theorem and nonmeasurable sets. -- 5. Small nonmeasurable sets. -- 6. Strange subsets of the Euclidean plane. -- 7. Some special constructions of nonmeasurable sets. -- 8. The Generalized Vitali construction. -- 9. Selectors associated with countable subgroups. -- 10. Selectors associated with uncountable subgroups. -- 11. Absolutely nonmeasurable sets in groups. -- 12. Ideals producing nonmeasurable unions of sets. -- 13. Measurability properties of subgroups of a given group. -- 14. Groups of rotations and nonmeasurable sets. -- 15. Nonmeasurable sets associated with filters. -- Appendix 1: Logical aspects of the existence of nonmeasurable sets. -- Appendix 2: Some facts from the theory of commutative groups. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliographical references (p. 317-333) and index. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on print version record. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Measure theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functional analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Set theory. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS |
| General subdivision | Calculus. |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS |
| General subdivision | Mathematical Analysis. |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functional analysis. |
| Source of heading or term | fast |
| Authority record control number | (OCoLC)fst00936061 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Measure theory. |
| Source of heading or term | fast |
| Authority record control number | (OCoLC)fst01013175 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Set theory. |
| Source of heading or term | fast |
| Authority record control number | (OCoLC)fst01113587 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Kharazishvili, A.B. |
| Title | Nonmeasurable sets and functions. |
| Edition | 1st ed. |
| Place, publisher, and date of publication | Amsterdam ; Boston : Elsevier, 2004 |
| International Standard Book Number | 0444516263 |
| -- | 9780444516268 |
| Record control number | (DLC) 2004049706 |
| -- | (OCoLC)55078412 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | North-Holland mathematics studies ; |
| Volume number/sequential designation | 195. |
| International Standard Serial Number | 0304-0208 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | ScienceDirect |
| Uniform Resource Identifier | <a href="http://www.sciencedirect.com/science/book/9780444516268">http://www.sciencedirect.com/science/book/9780444516268</a> |
| 856 4# - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="http://www.sciencedirect.com/science/publication?issn=03040208&volume=195">http://www.sciencedirect.com/science/publication?issn=03040208&volume=195</a> |
| Materials specified | Volltext |
| 938 ## - | |
| -- | ebrary |
| -- | EBRY |
| -- | ebr10177032 |
| 938 ## - | |
| -- | Ingram Digital eBook Collection |
| -- | IDEB |
| -- | 100888 |
| 938 ## - | |
| -- | EBSCOhost |
| -- | EBSC |
| -- | 132245 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | E(electronic)-Books |
| 994 ## - | |
| -- | C0 |
| -- | TEF |
No items available.
