UID:
almahu_9947367686302882
Format:
1 online resource (350 p.)
Edition:
1st ed.
ISBN:
1-281-00888-5
,
9786611008888
,
0-08-047976-6
Series Statement:
North-Holland mathematics studies, 195
Content:
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 invarian
Note:
Description based upon print version of record.
,
Cover; Contents; Preface; Chapter 1. The Vitali Theorem; Theorem 1; Theorem 2; Theorem 3; Theorem 4; Theorem 5; Theorem 6; Exercises; Chapter 2. The Bernstein Construction; Theorem 1; Theorem 2; Theorem 3; Theorem 4; Theorem 5; Exercises; Chapter 3. Nonmeasurable Sets Associated with Hamel Bases; Theorem 1; Theorem 2; Lemma 1; Lemma 2; Theorem 3; Theorem 4; Theorem 5; Theorem 6; Theorem 7; Exercises; Chapter 4. The Fubini Theorem and Nonmeasurable Sets; Theorem 1; Lemma 1; Lemma 2; Theorem 2; Theorem 3; Theorem 4; Exercises; Chapter 5. Small Nonmeasurable Sets; Theorem 1; Theorem 2; Theorem 3
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Theorem 4Lemma 1; Lemma 2; Theorem 5; Exercises; Chapter 6. Strange Subsets of the Euclidean Plane; Theorem 1; Lemma 1; Theorem 2; Theorem 3; Lemma 2; Lemma 3; Lemma 4; Theorem 4; Exercises; Chapter 7. Some Special Constructions of Nonmeasurable Sets; Theorem 1; Theorem 2; Lemma 1; Theorem 3; Exercises; Chapter 8. The Generalized Vitali Construction; Lemma 1; Lemma 2; Lemma 3; Lemma 4; Lemma 5; Theorem 1; Theorem 2; Exercises; Chapter 9. Selectors Associated with Countable Subgroups; Lemma 1; Lemma 2; Lemma 3; Lemma 4; Lemma 5; Lemma 6; Lemma 7; Theorem 1; Theorem 2; Theorem 3; Exercises
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Chapter 10. Selectors Associated with Uncountable SubgroupsTheorem 1; Theorem 2; Theorem 3; Exercises; Chapter 11. Absolutely Nonmeasurable Sets in Groups; Lemma 1; Lemma 2; Lemma 3; Theorem 1; Lemma 4; Lemma 5.; Theorem 2; Theorem 3; Theorem 4; Theorem 5; Theorem 6; Theorem 7; Exercises; Chapter 12. Ideals Producing Nonmeasurable Unions of Sets; Lemma 1; Theorem 1; Theorem 2; Theorem 3; Theorem 4; Lemma 2; Lemma 3; Lemma 4; Lemma 5; Theorem 5; Theorem 6; Theorem 7; Theorem 8; Theorem 9; Exercises; Chapter 13. Measurability Properties of Subgroups of a Given Group; Lemma 1; Lemma 2; Lemma 3
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Theorem 1Theorem 2; Theorem 3; Lemma 4; Lemma 5; Lemma 6; Lemma 7; Lemma 8; Theorem 4; Exercises; Chapter 14. Groups of Rotations and Nonmeasurable Sets; Lemma 1; Lemma 2; Lemma 3; Lemma 4; Theorem 1; Theorem 2; Exercises; Chapter 15. Nonmeasurable Sets Associated with Filters; Lemma 1; Lemma 2; Theorem 1; Lemma 3; Lemma 4; Lemma 5; Theorem 2; Exercises; Appendix 1 Logical Aspects of the Existence of Nonmeasurable Sets; Theorem 1; Theorem 2; Appendix 2 Some Facts From the Theory of Commutative Groups; Theorem 1; Theorem 2; Theorem 3; Theorem 4; Bibliography; Subject Index
,
English
Additional Edition:
ISBN 0-444-51626-3
Language:
English
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