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024 7 $a10.1007/978-3-031-17033-1
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035   $a(DE-He213)978-3-031-17033-1
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100   $a20220923d2022      u|             0
101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aNotes on Real Analysis and Measure Theory$b[electronic resource] $eFine Properties of Real Sets and Functions /$fby Alexander Kharazishvili
205   $a1st ed. 2022.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022.
215   $a1 online resource (256 pages)
225 1 $aSpringer Monographs in Mathematics,$x2196-9922
311   $a3-031-17032-6 
320   $aIncludes bibliographical references and index.
327   $aPreface -- 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.
330   $aThis monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.
410  0$aSpringer Monographs in Mathematics,$x2196-9922
606   $aMathematics
606   $aMathematics
606   $aFuncions de variables reals$2thub
606   $aTeoria de la mesura$2thub
608   $aLlibres electrònics$2thub
615  0$aMathematics.
615 14$aMathematics.
615  7$aFuncions de variables reals
615  7$aTeoria de la mesura
676   $a515.8
700   $aKharazishvili$b Alexander$01258282
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996490344103316
996   $aNotes on Real Analysis and Measure Theory$92915949
997   $aUNISA