This volume develops the classical theory of the Lebesgue integral and some of its applications. The integral is initially presented in the context of n-dimensional Euclidean space, following a thorough study of the concepts of outer measure and measure. A more general treatment of the integral, based on an axiomatic approach, is later given. Closely related topics in real variables, such as functions of bounded variation, the Riemann-Stieltjes integral, Fubini's theorem, L(p)) classes, and various results about differentiation are examined in detail. Several applications of the theory to a specific branch of analysis - harmonic analysis - are also provided.Among these applications are basic facts about convolution operators and Fourier series, including results for the conjugate function and the Hardy-Littlewood maximal function. "Measure and Integral: An Introduction to Real Analysis" provides an introduction to real analysis for student interested in mathematics, statistics, or probability. Requiring only a basic familiarity with advanced calculus, this volume is an excellent textbook for advanced undergraduate or first-year graduate student in these areas.
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讀後感
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評分
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用戶評價
碩士時隔壁math的phd實分析教材，據說齣自Zygmund的講義。非數學齣身，覺得也不算太難。課上大部分math phd都不會來。可能對數學係的phd有些簡單瞭。
评分這就是課本，真囧
评分這就是課本，真囧
评分這就是課本，真囧
评分這就是課本，真囧
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