03483nam 22005535 450 99649034410331620240221142958.03-031-17033-410.1007/978-3-031-17033-1(CKB)5840000000091737(MiAaPQ)EBC7101844(Au-PeEL)EBL7101844(DE-He213)978-3-031-17033-1(PPN)264953762(EXLCZ)99584000000009173720220923d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNotes on Real Analysis and Measure Theory[electronic resource] Fine Properties of Real Sets and Functions /by Alexander Kharazishvili1st ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (256 pages)Springer Monographs in Mathematics,2196-99223-031-17032-6 Includes bibliographical references and index.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.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.Springer Monographs in Mathematics,2196-9922MathematicsMathematicsFuncions de variables realsthubTeoria de la mesurathubLlibres electrònicsthubMathematics.Mathematics.Funcions de variables realsTeoria de la mesura515.8Kharazishvili Alexander1258282MiAaPQMiAaPQMiAaPQBOOK996490344103316Notes on Real Analysis and Measure Theory2915949UNISA