Measure and Integration

This book covers the material of a one year course in real analysis.  It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom.  Each chapter contains numerous examples and an extensive problem set which expands considerably the breadth of the material covered in the text.  Hints are included for some of the more difficult problems.                

List of contents

Rings of sets.- Measurability.- Integrals and Measures.- Convergence Theorems for Lebesgue Integrals.- Existence and Uniqueness of Measures.- Signed Measures, Complex Measures and Absolute Continuity.- Measure and Topology.- Product Measures.- The Lp Spaces.- Fourier Analysis.- Standard Measure Spaces.              

About the author

Hari Bercovici is a Professor in the Department of Mathematics at Indiana University Bloomington.  His research interests include functional analysis, operator theory, and free probability.
Carl Pearcy is an Emeritus Professor in Mathematics at Texas A&M University. His research interest is in functional analysis.                     

Summary

                 

Additional text

“The book is a perfect introduction for graduate students into the theory of measure and Lebesgue integration. It is written in a very pedagogical way providing in each chapter many examples and a long collection of problems with a number of hints for the more challenging ones.” (Oscar Blasco, zbMATH 1337.28001, 2016)

Report

"The book is a perfect introduction for graduate students into the theory of measure and Lebesgue integration. It is written in a very pedagogical way providing in each chapter many examples and a long collection of problems with a number of hints for the more challenging ones." (Oscar Blasco, zbMATH 1337.28001, 2016)

Product details

• Authors: Har Bercovici, Hari Bercovici, Arle Brown, Arlen Brown, Carl Pearcy
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2018
• EAN: 9783319804804
• ISBN: 978-3-31-980480-4
• No. of pages: 300
• Dimensions: 157 mm x 236 mm x 19 mm
• Weight: 476 g
• Illustrations: XI, 300 p.
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Reelle Analysis, Real-Variablen, measure theory, Mathematics and Statistics, Real Functions, Functions of real variables, Measure and Integration, Fourier Analysis, Real analysis, real variables, Fourier series, Standard measure space, Functional algebra, Maximal function