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Set theoretical aspects of real analysis / Alexander B. Kharazishvili, Tbilisi State University, Georgia.

By: Contributor(s): Material type: TextTextLanguage: English Series: Monographs and research notes in mathematicsPublisher: Boca Raton, Florida : CRC Press, Taylor & Francis Group, [2015]Copyright date: ©2015Description: xxii, 433 p. ; 24 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9781482242010 (alk. paper)
  • 148224201X (alk. paper)
Subject(s): DDC classification:
  • 514/.7 23
LOC classification:
  • QA300 .K43 2015
Contents:
1. ZF theory and some point sets on the real line -- 2. Countable versions of AC and real analysis -- 3. Uncountable versions of AC and Lebesgue nonmeasurable sets -- 4. The Continuum Hypothesis and Lebesgue nonmeasurable sets -- 5. Measurability properties of sets and functions -- 6. Radon measures and nonmeasurable sets -- 7. Real-valued step functions with strange measurability properties -- 8. A partition of the real line into continuum many thick subsets -- 9. Measurability properties of Vitali sets -- 10. A relationship between the measurability and continuity of real-valued functions -- 11. A relationship between absolutely nonmeasurable functions and Sierpiński-Zygmund type functions -- 12. Sums of absolutely nonmeasurable injective functions -- 13. A large group of absolutely nonmeasurable additive functions -- 14. Additive properties of certain classes of pathological functions -- 15. Absolutely nonmeasurable homomorphisms of commutative groups -- 16. Measurable and nonmeasurable sets with homogeneous sections -- 17. A combinatorial problem on translation invariant extensions of the Lebesgue measure -- 18. Countable almost invariant partitions of G-spaces -- 19. Nonmeasurable unions of measure zero sections of plane sets -- 20. Measurability properties of well-orderings.
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Item type Current library Call number Copy number Status Date due Barcode
წიგნი წიგნი ეროვნული სამეცნიერო ბიბლიოთეკა 1 საცავი. 1 კორპ. 517 (Browse shelf(Opens below)) 2E64000 Available 2021-8257

"A Chapman & Hall book."

Includes bibliographical references: p. 411-428 and index.

1. ZF theory and some point sets on the real line -- 2. Countable versions of AC and real analysis -- 3. Uncountable versions of AC and Lebesgue nonmeasurable sets -- 4. The Continuum Hypothesis and Lebesgue nonmeasurable sets -- 5. Measurability properties of sets and functions -- 6. Radon measures and nonmeasurable sets -- 7. Real-valued step functions with strange measurability properties -- 8. A partition of the real line into continuum many thick subsets -- 9. Measurability properties of Vitali sets -- 10. A relationship between the measurability and continuity of real-valued functions -- 11. A relationship between absolutely nonmeasurable functions and Sierpiński-Zygmund type functions -- 12. Sums of absolutely nonmeasurable injective functions -- 13. A large group of absolutely nonmeasurable additive functions -- 14. Additive properties of certain classes of pathological functions -- 15. Absolutely nonmeasurable homomorphisms of commutative groups -- 16. Measurable and nonmeasurable sets with homogeneous sections -- 17. A combinatorial problem on translation invariant extensions of the Lebesgue measure -- 18. Countable almost invariant partitions of G-spaces -- 19. Nonmeasurable unions of measure zero sections of plane sets -- 20. Measurability properties of well-orderings.

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