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Real Analysis (4th Edition) by Halsey Royden, Patrick Fitzpatrick

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About this book :-
Real Analysis (4th Edition) written by Halsey Royden, Patrick Fitzpatrick .
The first three editions of H.L.Royden's Real Analysis have contributed to the education of generations of mathematical analysis students. This fourth edition of Real Analysis preserves the goal and general structure of its venerable predecessors-to present the measure theory,integration theory, and functional analysis that a modem analyst needs to know.
The book is divided the three parts: Part I treats Lebesgue measure and Lebesgue integration for functions of a single real variable; Part II treats abstract spaces-topological spaces, metric spaces, Banach spaces, and Hilbert spaces; Part III treats integration over general measure spaces, together with the enrichments possessed by the general theory in the presence of topological, algebraic, or dynamical structure.
The material in Parts II and III does not formally depend on Part I. However, a careful treatment of Part I provides the student with the opportunity to encounter new concepts in a familiar setting, which provides a foundation and motivation for the more abstract concepts developed in the second and third parts. Moreover, the Banach spaces created in Part I, the LP spaces, are one of the most important classes of Banach spaces. The principal reason for establishing the completeness of the LP spaces and the characterization of their dual spaces is to be able to apply the standard tools of functional analysis in the study of functionals and operators on these spaces. The creation of these tools is the goal of Part II.
This new edition contains 50% more exercises than the previous edition Fundamental results, including Egoroff s Theorem and Urysohn's Lemma are now proven in the text.

Book Detail :-
Title: Real Analysis
Edition: 4th
Author(s): Halsey Royden, Patrick Fitzpatrick
Publisher: Prentice Hall
Year: 2010
Pages: 516
Type: PDF
Language: English
ISBN: 013143747X,9780131437470
Country: US
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About Author :-
The author Halsey Lawrence Royden Jr. was born in 1928. Royden was an American mathematician, specializing in complex analysis on Riemann surfaces, several complex variables, and complex differential geometry.[1] Royden is the author of a popular textbook on Real Analysis.
After study at Phoenix College, Royden transferred in 1946 to Stanford University, where he received his bachelor's degree in 1948 and his master's degree in 1949 with a master's thesis written under the supervision of Donald Spencer. Royden received his Ph.D. in 1951 at Harvard University under the supervision of Lars Ahlfors with thesis Harmonic functions on open Riemann surfaces.[3] At Stanford University he became an assistant professor in 1951, an associate professor in 1953, and a full professor in 1958. In addition to serving on the faculty of the mathematics department, for Stanford's School of Humanities and Sciences he was in 1962–1965 associate dean, in 1968–1969 executive dean (acting dean until the vacancy was resolved), and in 1973–1981 dean. In 1981 he resigned as dean to work full-time as a mathematics professor.[4] He was on the editorial board of the Pacific Journal of Mathematics for the five years from 1956 to 1960. Royden was a Visiting Scholar at the Institute for Advanced Study in Princeton for 3 months in the fall of 1969, 3 months in the spring of 1974, and for the academic year 1982–1983

The author Patrick M. Fitzpatrick was born in March 1946, Youghal, Republic of Ireland. He complete his B.A. in Mathematics, Rutgers University (1966) and Ph.D. in Mathematics, Rutgers University (1966)
He done his B.S. in Mathematics, 1966, Rutgers University and Ph.D. in Mathematics, 1971, Rutgers University
He start his career as Chair, Department of Mathematics, UMd (1996–2007) then Associate Chair for Undergraduate Studies, UMd (1994–1996). He start as Assistant Professor, UMd (1975–1984) and Professor, UMd (1984)
He also work as Visiting Assistant Professor, Rutgers University (1972–1973) and Visiting Member, Courant Institute of Mathematical Sciences, N.Y.U (1971–1972) and Visiting Member, Institute for Physical Sciences and Technology, UMd (1977–1986)
My present research interests center on the study of topological methods in nonlinear operator theory, with particular interest in the study of bifurcation of solutions of parametrized families of nonlinear partial differential equations. One aspect of this has been the development of a topological degree for nonlinear Fredholm mappings. The essential novelty of this degree is that it presents a new, precise description of the homotopy property of degree that is needed to establish global bofurcation results for one parameter families of such mappings.

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Book Contents :-
Real Analysis (4th Edition) written by Halsey Royden, Patrick Fitzpatrick cover the following topics.
I Lebesgue Integration for Functions of a Single Real Variable
0. Preliminaries on Sets, Mappings, and Relations
1. The Real Numbers: Sets, Sequences, and Functions
2. Lebesgue Measure
3. Lebesgue Measurable Functions
4. Lebesgue Integration
5. Lebesgue Integration: Further Topics
6. Differentiation and Integration
7. The I)' Spaces: Completeness and Approximation
8. The I)' Spaces: Duality and Weak Convergence
II Abstract Spaces: Metric, Topological, Banach, and Hilbert Spaces
9. Metric Spaces: General Properties
10. Metric Spaces: Three Fundamental Theorems
11. Topological Spaces: General Properties
12. Topological Spaces: Three Fundamental Theorems
13. Continuous Linear Operators Between Banach Spaces
14. Duality for Normed Linear Spaces
15. Compactness Regained: The Weak Topology
16. Continuous Linear Operators on Hilbert Spaces
III Measure and Integration: General Theory
17. General Measure Spaces: Their Properties and Construction
18. Integration Over General Measure Spaces
19. General LP Spaces: Completeness, Duality, and Weak Convergence
20. The Construction of Particular Measures
21. Measure and Topology
22. Invariant Measures


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