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real analysis: measure theory, integration, hilbert spaces [pdf]

### Real Analysis: Measure Theory, Integration, Hilbert Spaces by Elias M. Stein, Rami Shakarchi

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Real Analysis: Measure Theory, Integration, Hilbert Spaces written by Elias M. Stein, Rami Shakarchi
Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science.
After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises.
As with the other volumes in the series, Real Analysis is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels.
(Elias M. Stein, Rami Shakarchi)

Book Detail :-
Title: Real Analysis: Measure Theory, Integration, Hilbert Spaces
Edition:
Author(s): Elias M. Stein, Rami Shakarchi
Publisher: Princeton University Press
Series: Princeton Lectures in Analysis
Year: 2005
Pages: 423
Type: PDF
Language: English
ISBN: 0691113866,9780691113869
Country: US
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Author Elias Menachem Stein was an American mathematician who was famous because of his work in the field of harmonic analysis. He was professor of Mathematics at Princeton University from 1963 until his death in 2018.
Author Menachem Stein was born in Antwerp Belgium, to Elkan Stein and Chana Goldman, Ashkenazi Jews from Belgium. In 1940, the Stein family move to the United States. He graduated from Stuyvesant High School in 1949, where he was classmates with future Fields Medalist Paul Cohen, before moving on to the University of Chicago for college. In 1955, Stein earned a Ph.D. from the University of Chicago under the direction of Antoni Zygmund. He began teaching in MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton.
Stein worked primarily in the field of harmonic analysis, and made contributions in both extending and clarifying Calderón–Zygmund theory. These include Stein interpolation, the Stein maximal principle, Stein complementary series representations, Nikishin–Pisier–Stein factorization in operator theory, the Tomas–Stein restriction theorem in Fourier analysis, the Kunze–Stein phenomenon in convolution on semisimple groups, the Cotlar–Stein lemma concerning the sum of almost orthogonal operators, and the Fefferman–Stein theory of the Hardy space and the space of functions of bounded mean oscillation.

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Book Contents :-
Real Analysis: Measure Theory, Integration, Hilbert Spaces written by Elias M. Stein, Rami Shakarchi cover the following topics.
Foreword
0-Introduction
1. Measure Theory
2. Integration Theory
3. Differentiation and Integration
4. Hilbert Spaces: An Introduction
5. Hilbert Spaces: Several Examples
6. Abstract Measure and Integration Theory
7. Hausdor® Measure and Fractals
Notes and References
Bibliography
Symbol Glossary
Index

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