Measure and Integration: Springer Undergraduate Mathematics Series
Autor Satish Shirali, Harkrishan Lal Vasudevaen Limba Engleză Paperback – 23 sep 2019
This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis.
Proceeding at a leisurely, student-friendly pace, the authors begin by recalling elementary notions of real analysis before proceeding to measure theory and Lebesgue integration. Further chapters cover Fourier series, differentiation, modes of convergence, and product measures. Noteworthy topics discussed in the text include Lp spaces, the Radon–Nikodým Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems.
This textbook, based on extensive teaching experience, is written for senior undergraduate and beginning graduate students in mathematics. With each topic carefully motivated and hints to more than 300 exercises, it is the ideal companion for self-study or use alongside lecture courses.
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Specificații
ISBN-13: 9783030187460
ISBN-10: 3030187462
Pagini: 545
Ilustrații: XII, 598 p.
Dimensiuni: 155 x 235 mm
Greutate: 0.84 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria Springer Undergraduate Mathematics Series
Locul publicării:Cham, Switzerland
ISBN-10: 3030187462
Pagini: 545
Ilustrații: XII, 598 p.
Dimensiuni: 155 x 235 mm
Greutate: 0.84 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria Springer Undergraduate Mathematics Series
Locul publicării:Cham, Switzerland
Cuprins
1 Preliminaries.- 2 Measure in Euclidean Space.- 3 Measure Spaces and Integration.- 4 Fourier Series.- 5 Differentiation.- 6 Lebesgue Spaces and Modes of Convergence.- 7 Product Measure and Completion.- 8 Hints.- References.- Index.
Notă biografică
Satish Shirali's research interest are in Banach *algebras, elliptic boundary value problems, fuzzy measures, and Harkrishan Vasudeva's interests are in functional analysis. This is their fourth joint textbook, having previous published An Introduction to Mathematical Analysis (2014), Multivariable Analysis (2011) and Metric Spaces (2006). Shirali is also the author of the book A Concise Introduction to Measure Theory (2018), and Vasudeva is the author of Elements of Hilbert Spaces and Operator Theory (2017) and co-author of An Introduction to Complex Analysis (2005).
Textul de pe ultima copertă
This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis.
Proceeding at a leisurely, student-friendly pace, the authors begin by recalling elementary notions of real analysis before proceeding to measure theory and Lebesgue integration. Further chapters cover Fourier series, differentiation, modes of convergence, and product measures. Noteworthy topics discussed in the text include Lp spaces, the Radon–Nikodým Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems.
This textbook, based on extensive teaching experience, is written for senior undergraduate and beginning graduate students in mathematics. With each topic carefully motivated and hints to more than 300 exercises, it is the ideal companion for self-study or use alongside lecture courses.
Caracteristici
Supplements the abstract theory with a great amount of motivation, explanations and concrete examples Includes background on metric spaces and mathematical analysis Over 300 exercises with hints