A Course on Integration Theory including more than 150 exercises with detailed answers /

• Main Author: Lerner, Nicolas (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2014.
• Subjects: Mathematics.; Measure theory.; Functions of real variables.; Real Functions.; Measure and Integration.

This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrab...

Table of Contents:

• 1 Introduction
• 2 General theory of integration
• 3 Construction of the Lebesgue measure on R^d
• 4 Spaces of integrable functions
• 5 Integration on a product space
• 6 Diffeomorphisms of open subsets of R^d and integration
• 7 Convolution
• 8 Complex measures
• 9 Harmonic analysis
• 10 Classical inequalities.