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Mathematics Information Resource Centre, Department of Mathematics, IISc, Bangalore.

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Modern Real Analysis / by William P. Ziemer.

By: Material type: TextTextSeries: Graduate Texts in Mathematics ; 278Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Edition: 2nd ed. 2017Description: 1 online resource (XI, 382 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783319646299
Subject(s): Additional physical formats: Print version:: Modern real analysis.; Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification:
  • 515.8 23
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.
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.
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Holdings
Item type Current library Home library Collection Call number Status Barcode
Book Book MATH-LiB General Stack NBHM Library Procurement 515.8 P17 (Browse shelf(Opens below)) In transit from MATH-LiB to NBHM Library since 11/29/2023 CP8211
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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.

Description based on publisher-supplied MARC data.

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