Notes on real analysis and measure theory : fine properties of real sets and functions

Notes on real analysis and measure theory : fine properties of real sets and functions / Alexander Kharazishvili.

This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. T...

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Bibliographic Details
Main Author: Kharazishvili, A. B. (Author)
Format: eBook
Language:English
Published: Cham : Springer, [2022]
Series:Springer monographs in mathematics.
Subjects:
Functions of real variables.
Measure theory.
Teoría de la medida
Funciones de variables reales
Functions of real variables
Measure theory
Funcions de variables reals.
Teoria de la mesura.
Electronic books.
Llibres electrònics.
Online Access:Click for online access
Table of Contents:
  • Preface
  • 1. Real-Valued Semicontinuous Functions
  • 2. The Oscillations of Real-Valued Functions
  • 3. Monotone and Continuous Restrictions of Real-Valued Functions
  • 4. Bijective Continuous Images of Absolute Null Sets
  • 5. Projective Absolutely Nonmeasurable Functions
  • 6. Borel Isomorphisms of Analytic Sets
  • 7. Iterated Integrals of Real-Valued Functions of Two Real Variables
  • 8. The Steinhaus Property, Ergocidity, and Density Points
  • 9. Measurability Properties of H-Selectors and Partial H-Selectors
  • 10. A Decomposition of an Uncountable Solvable Group into Three Negligible Sets
  • 11. Negligible Sets Versus Absolutely Nonmeasurable Sets
  • 12. Measurability Properties of Mazurkiewicz Sets
  • 13. Extensions of Invariant Measures on R
  • A. A Characterization of Uncountable Sets in Terms of their Self-Mappings
  • B. Some Applications of Peano Type Functions
  • C. Almost Rigid Mathematical Structures
  • D. Some Unsolved Problems in Measure Theory
  • Bibliography
  • Index.

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