Shirali / Vasudeva Measure and Integration

Erscheinungsjahr 2019
ISBN: 978-3-030-18747-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 598 Seiten

Reihe: Springer Undergraduate Mathematics Series

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  spaces, the Radon–Nikody´m 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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Shirali, Satish

Vasudeva, Harkrishan Lal

Inhaltsverzeichnis

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.

Über Autor(innen)

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).