Modern Real Analysis
Springer International Publishing (Verlag)
978-3-319-64628-2 (ISBN)
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.
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.
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 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)
“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)
| Erscheinungsdatum | 06.01.2018 |
|---|---|
| Reihe/Serie | Graduate Texts in Mathematics |
| Co-Autor | Monica Torres |
| Zusatzinfo | XI, 382 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 754 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Functional Analysis • Functional analysis & transforms • Functional analysis & transforms • graduate level analysis • Integral calculus & equations • Integral calculus & equations • Lebesque measure • Mathematics • mathematics and statistics • measure and integration • measure theory • modern real analysis • modern real analysis textbook adoption • Real analysis, real variables • real functions • Ziemer William textbook |
| ISBN-10 | 3-319-64628-1 / 3319646281 |
| ISBN-13 | 978-3-319-64628-2 / 9783319646282 |
| Zustand | Neuware |
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