Introduction to Measure Theory and Integration

• Main Authors: Ambrosio, Luigi (Author), Prato, Giuseppe Da (Author), Mennucci, Andrea (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Pisa : Edizioni della Normale, 2011.
• Series: Appunti/Lecture Notes ; 10
• Subjects: Mathematics.; Measure theory.; Measure and Integration.

This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of the course was to present, in a quick but rigorous way, the modern point...

Table of Contents:

• Measure spaces
• Integration
• Spaces of measurable functions
• Hilbert spaces
• Fourier series
• Operations on measures
• The fundamental theorem of integral calculus
• Operations on measures
• Appendix: Riesz representation theorem of the dual of C(K) and integrals depending on a parameter
• Solutions to the exercises.