TY  - BOOK
AU  - Ziemer,William P.
TI  - Modern Real Analysis
T2  - Graduate Texts in Mathematics,
SN  - 9783319646299
U1  - 515.8 23
PY  - 2017///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Functional analysis
KW  - Functions of real variables
KW  - Measure theory
KW  - Real Functions
KW  - Functional Analysis
KW  - Measure and Integration
N1  - 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
N2  - 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
ER  -