Measure and Integration

Beschreibung

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 L^p 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.
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 L^p 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.
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

Autor*in

Satish Shirali

Themen in »Measure and Integration«

Measure theory Integration theory Lebesgue measure Fourier series Fubini theorem Tonelli theorem Lp spaces Vitali covering theorem Radon-Nikodym theorem Product measure Cantor set Bounded variation Absolute continuity

Stimmen zu »Measure and Integration«

Details

Link teilen