Notes on Real Analysis and Measure Theory : Fine Properties of Real Sets and Functions / by Alexander Kharazishvili

By:

Kharazishvili, Alexander [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Monographs in MathematicsPublisher: Cham : Springer International Publishing, 2022Publisher: Cham : Imprint: Springer, 2022Edition: 1st ed. 2022Description: 1 Online-Ressource(XI, 253 p.)ISBN:

9783031170331

Subject(s):

Mathematics

Additional physical formats: 9783031170324 | 9783031170348 | 9783031170355 | Erscheint auch als: 9783031170324 Druck-Ausgabe | Erscheint auch als: 9783031170348 Druck-Ausgabe | Erscheint auch als: 9783031170355 Druck-AusgabeDOI: DOI: 10.1007/978-3-031-17033-1Online resources:

Summary: 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.Summary: 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. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.PPN: PPN: 1817571273Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

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