Modern Real Analysis (Graduate Texts in Mathematics, 278) by Ziemer (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “This book provides an accessible self-contained introduction to modern real analysis suitable for graduate students with an understanding of advanced calculus. It may also provide a useful reference for more experienced mathematicians. The focus of the book is on measure and integration, which are nicely connected to closely related topics such as bounded variations and absolutely continuous functions representations theorems for linear functionals, Sovolev spaces and distribution.” (Gareth Speight, Mathematical Reviews, October, 2018)​ From the Back Cover 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. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Das Buch kann eigenständig gelesen werden. Ziemer führt gekonnt auf hohem Niveau in die Real Analysis ein. Einführende Kapitel zu FA und GF sind auch dabei. Klare Empfehlung.Amazon schnelle Lieferung und Buch wie beschrieben.

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