Essentials of Integration Theory for Analysis de Daniel W. Stroock

Essentials of Integration Theory for Analysis: Graduate Texts in Mathematics, cartea 262

Autor Daniel W. Stroock

en Limba Engleză Paperback – 25 noi 2021

When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhäuser title by the same author, A Concise Introduction to the Theory of Integration. Appropriate as a primary text for a one-semester graduate course in integration theory, this GTM is also useful for independent study. A complete solutions manual is available for instructors who adopt the text for their courses. This second edition has been revised as follows: §2.2.5 and §8.3 have been substantially reworked. New topics have been added. As an application of the material about Hermite functions in §7.3.2, the author has added a brief introduction to Schwartz's theory of tempered distributions in §7.3.4. Section §7.4 is entirely new and contains applications, including the Central Limit Theorem, of Fourier analysis to measures. Related to this are subsections §8.2.5 and §8.2.6, where Lévy's Continuity Theorem and Bochner's characterization of the Fourier transforms of Borel probability on ℝ^N are proven. Subsection 8.1.2 is new and contains a proof of the Hahn Decomposition Theorem. Finally, there are several new exercises, some covering material from the original edition and others based on newly added material.

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Specificații

ISBN-13: 9783030584801
ISBN-10: 3030584801
Pagini: 285
Ilustrații: XVI, 285 p. 1 illus.
Dimensiuni: 155 x 235 mm
Ediția:2nd ed. 2020
Editura: Springer International Publishing
Colecția Springer
Seria Graduate Texts in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

Preface.- Notation.- 1. The Classical Theory.-2. Measures. -3. Lebesgue Integration.-4. Products of Measures.-5. Changes of Variable.-6. Basic Inequalities and Lebesgue Spaces.-7. Hilbert Space and Elements of Fourier Analysis.-8. Radon–Nikodym, Hahn, Daniell Integration, and Carathéodory- Index.

Notă biografică

Daniel W. Stroock is Emeritus professor of mathematics at MIT. He is a respected mathematician in the areas of analysis, probability theory and stochastic processes. Prof. Stroock has had an active career in both the research and education. From 2002 until 2006, he was the first holder of the second Simons Professorship of Mathematics. In addition, he has held several administrative posts, some within the university and others outside. In 1996, the AMS awarded him together with his former colleague jointly S.R.S. Varadhan the Leroy P. Steele Prize for seminal contributions to research in stochastic processes. Finally, he is a member of both the American Academy of Arts and Sciences, the National Academy of Sciences and a foreign member of the Polish Academy of Arts and Sciences.

Textul de pe ultima copertă

When the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhäuser title by the same author, A Concise Introduction to the Theory of Integration. Appropriate as a primary text for a one-semester graduate course in integration theory, this GTM is also useful for independent study. A complete solutions manual is available for instructors who adopt the text for their courses. This second edition has been revised as follows: §2.2.5 and §8.3 have been substantially reworked. New topics have been added. As an application of the material about Hermite functions in §7.3.2, the author has added a brief introduction to Schwartz's theory of tempered distributions in §7.3.4. Section §7.4 is entirely new and contains applications, including the Central Limit Theorem, of Fourier analysis to measures. Related to this are subsections §8.2.5 and §8.2.6, where Lévy's Continuity Theorem and Bochner's characterization ofthe Fourier transforms of Borel probability on ℝ^N are proven. Subsection 8.1.2 is new and contains a proof of the Hahn Decomposition Theorem. Finally, there are several new exercises, some covering material from the original edition and others based on newly added material.
From the reviews of the first edition:
“The presentation is clear and concise, and detailed proofs are given. … Each section also contains a long and useful list of exercises. … The book is certainly well suited to the serious student or researcher in another field who wants to learn the topic. …the book could be used by lecturers who want to illustrate a standard graduate course in measure theory by interesting examples from other areas of analysis.” (Lars Olsen, Mathematical Reviews 2012)
“…It will help the reader to sharpen his/her sensitivity to issues of measure theory, and to renew his/her expertise in integration theory.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1228, 2012)

Caracteristici

Solutions manual is available to instructors who adopt the textbook for their course Second edition revised with new topics, some reworked text, new exercises Suitable for a one-semester graduate course in integration theory as well as for independent study Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material

Recenzii

From the reviews:
“This volume is an appropriate text for a one-semester graduate course in integration theory and is complemented by the addition of several problems related to the new material. … This volume should become a new relevant reference for integration theory. It will help the reader to sharpen his/her sensitivity to issues of measure theory, and to renew his/hers expertise in integration theory. … warmly recommends the book with confidence to anyone who is interested in understanding modern integration theory.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1228, 2012)
“This is a book in measure theory at the graduate level. … The presentation is clear and concise, and detailed proofs are given. … Each section also contains a long and useful list of exercises. … The book is certainly well suited to the serious student or researcher in another field who wants to learn the topic. … the book could be used by lecturers who want to illustrate a standard graduate course in measure theory by interesting examples from other areas of analysis.” (Lars Olsen, Mathematical Reviews, Issue 2012 h)