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商品描述
This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations.
This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.
商品描述(中文翻譯)
這本一年級研究生的教材是一本關於實分析的綜合資源，基於現代的測度與積分處理。內容以明確且自足的方式呈現，概念從簡單到困難自然地進展。書中涵蓋了幾個創新的主題，包括測度的微分、泛函分析的元素、Riesz 表示定理、Schwartz 分佈、面積公式、Sobolev 函數及其在調和函數中的應用。這些主題的選擇共同構成了實分析的堅實基礎，特別適合有意進一步研究偏微分方程的學生。
《現代實分析》（Modern Real Analysis）第二版包含了許多實質性的改進，包括增加了練習技術的問題，以及一個全新的部分專門探討 Lebesgue 積分與不當積分之間的關係。這本教材針對具備高級微積分理解的研究生，同時也會吸引更有經驗的數學家作為有用的參考資料。
作者簡介
William P. Ziemer is Professor Emeritus of Mathematics at Indiana University, and is the author of the highly influential GTM (vol. 120), Weakly Differentiable Functions.
Monica Torres is Associate Professor of Mathematics at Purdue University, specializing in geometric measure theory and partial differential equations.
作者簡介(中文翻譯)
威廉·P·齊默是印第安納大學的數學榮譽教授，也是影響深遠的GTM（第120卷）《弱可微函數》的作者。
莫妮卡·托雷斯是普渡大學的數學副教授，專注於幾何測度論和偏微分方程。
