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Modern Real Analysis

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概要 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 na...tural 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.    .続きを見る
目次 Preface
1. Preliminaries
2. Real, Cardinal and Ordinal Numbers
3. Elements of Topology
4. Measure Theory
5. Measurable Functions
6. Integration
7. Differentiation
8. Elements of Functional Analysis
9. Measures and Linear Functionals
10. Distributions
11. Functions of Several Variables
Bibliography
Index.
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2017 English/International
Full text available from SpringerLink ebooks - Mathematics and Statistics without Lecture Notes (2017)

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登録日 2020.06.27
更新日 2021.05.09