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
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
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).
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–Nikodym 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.
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.
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–Nikodym 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.
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-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.
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).
Über den Autor
¿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).
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.
Klappentext
This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis.
rn
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-Nikody¿m Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems.
rn
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.
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
