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Synopsis
Contents: Infinite Sets; Point Sets; Measurable Sets; Measurable Functions; The Lebesgue Integral of a Bounded Function; Summable Functions; Square-Summable Functions; Functions of Finite Variation - The Stieltjes Integral; Absolutely Continuous Functions - The Indefinite Lebesgue Integral; Index. Real analysis (traditionally, the theory of functions of a real variable) is a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real numbers, and continuity, smoothness and related properties of real-valued functions.
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Theory of Functions of a Real Variable Volume 1
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