Titlebook: A Course in Functional Analysis and Measure Theory; Vladimir Kadets Textbook 2018 Springer Nature Switzerland AG 2018 MSC (2010): 46-01, 4

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Reihe Interkulturelle Philosophiee intrinsic metric of a surface are studied), and also, it goes without saying, in topology courses. For this reason, we only briefly recall the well-known definitions and facts, discuss the terminology and notation adopted in this book, while dwelling in more detail on issues that possibly are not treated in other courses.

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https://doi.org/10.1007/978-3-476-05832-4algebras of sets; Borel sets; finite and countable additivity of measures; atoms, atomic and non-atomic measures; extension of measures; the Lebesgue measure on the interval and on the real line; Lebesgue’s theorem on the differentiability of monotone functions.

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Reihe Interkulturelle Philosophie analogy with the Riemann integral, in this book the theory of the Lebesgue integral is treated on the basis of Fréchet’s definition, namely, by means of the convergent integral sums analogous to the Riemann integral sums. One of the advantages of this approach is the simplicity with which this definition extends to vector-valued functions.

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Reihe Interkulturelle Philosophie traditionally regarded as one of the “fundamental principles of functional analysis”. Such “fundamental principles” also include the geometric form of the Hahn–Banach theorem (Chapter 9), Banach’s inverse operator theorem, the open mapping and the closed graph theorems, as well as the Banach–Steinhaus theorem (Chapter 10).