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020 a| 9780080479767;

020 a| 0080479766 (E-Book)c| USD 176.00 Retail Price (Sony Electronics)9| Active Record;

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100 1 a| Kharazishvili, Alexandere| Author?| UNAUTHORIZED;

245 10 a| Nonmeasurable Sets and Functionsh| [electronic resource];

250 a| Revised;

440 0 a| NHMS/North-Holland Mathematics Studies;

506 a| Available only to authorized users.;

520 8 a| Annotationb| 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.;

538 a| Mode of access: World Wide Web;

650 4 a| Functional Analysis;

650 4 a| Measure Theory;

650 4 a| Set Theory;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from eBook - Mathematics pre-2007u| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Fbookseries%2F03040208%2F195;

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998 a| 6597313;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6597313-1001l| JNETm| JOYNERr| Ys| Yt| JNESSBKu| 7/18/2025x| EBOOKz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6597313-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 7/18/2025x| EBOOKz| HERESOURCE;

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Nonmeasurable Sets and Functions

Author/creator	Kharazishvili, Alexander Author
Format	Electronic
Edition	Revised
Publication Info	Elsevier Science [Imprint] San Diego : Elsevier Science & Technology Books Los Angeles : Sony Electronics [Distributor]
Supplemental Content	Full text available from eBook - Mathematics pre-2007
Subjects	Functional Analysis Measure Theory Set Theory

Series	NHMS/North-Holland Mathematics Studies
Summary	Annotation 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.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
ISBN	9780080479767
ISBN	0080479766 (E-Book) Active Record
Stock number	00991439

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