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Titlebook: Notes on Real Analysis and Measure Theory; Fine Properties of R Alexander Kharazishvili Book 2022 The Editor(s) (if applicable) and The Aut

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书目名称Notes on Real Analysis and Measure Theory
副标题Fine Properties of R
编辑Alexander Kharazishvili
视频video
概述This monograph gives an up-to-date account of the fine properties of real sets and functions.Stresses the relationship between real analysis and descriptive set theory.Gives the reader a self-containe
丛书名称Springer Monographs in Mathematics
图书封面Titlebook: Notes on Real Analysis and Measure Theory; Fine Properties of R Alexander Kharazishvili Book 2022 The Editor(s) (if applicable) and The Aut
描述.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..
出版日期Book 2022
关键词Alexander Kharazishvili; Strange Functions in Real Analysis; Real Analysis textbook; Measure Theory tex
版次1
doihttps://doi.org/10.1007/978-3-031-17033-1
isbn_softcover978-3-031-17035-5
isbn_ebook978-3-031-17033-1Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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Iterated Integrals of Real-Valued Functions of Two Real Variables,assumed to be measurable with respect to the two-dimensional Lebesgue measure λ. on the plane ℝ., but they have the property that their corresponding iterated integrals exist and are equal to each other. Close connections of this property with certain purely set-theoretical aspects are highlighted.
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Negligible Sets Versus Absolutely Nonmeasurable Sets, interested in the behavior of certain kinds of sets with respect to such measures. Actually, we will be concerned below with some unexpected relationships between so-called negligible subsets and absolutely nonmeasurable subsets of uncountable solvable groups.
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Real-Valued Semicontinuous Functions,Let . be a topological space, x. be a point of E, and let f : E → ℝ be a function. According to the well-known definition (see, e.g., [37, 51, 74, 111, 112]), f is said to be . at x. if, for any real ε > 0, there exists a neighborhood ?(x.) such that.
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The Oscillations of Real-Valued Functions,Let . be an arbitrary topological space. In this chapter, we will be dealing with various real-valued functions defined on some subsets of . (i.e., partial real-valued functions on .).
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