Measure and Integration

Description

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. Front Matter ....Pages i-xii Preliminaries (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 1-42 Measure in Euclidean Space (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 43-108 Measure Spaces and Integration (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 109-162 Fourier Series (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 163-209 Differentiation (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 211-336 Lebesgue Spaces and Modes of Convergence (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 337-374 Product Measure and Completion (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 375-404 Hints (Satish Shirali, Harkrishan Lal Vasudeva)....Pages 405-590 Back Matter ....Pages 591-598