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Modern real analysis

By: Material type: TextTextSeries: Graduate texts in mathematics; No. 278Publication details: Springer 2017 ChamEdition: 2ndDescription: xi, 382 p. Includes bibliographical references and indexISBN:
  • 9783319646282
Subject(s): DDC classification:
  • 515.8 Z4M6
Summary: 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. https://www.springer.com/gp/book/9783319646282
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Item type Current library Item location Collection Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 28-A / Slot 1382 (0 Floor, East Wing) Non-fiction General Stacks 515.8 Z4M6 (Browse shelf(Opens below)) Available 201408

Table of contents
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.

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.

https://www.springer.com/gp/book/9783319646282

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