Lectures on Functional Analysis and the Lebesgue Integral

• Main Author: Komornik, Vilmos (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2016.
• Series: Universitext,
• Subjects: Mathematics.; Approximation theory.; Functional analysis.; Measure theory.; Functional Analysis.; Measure and Integration.; Approximations and Expansions.

This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and th...

Table of Contents:

• Some papers of general interest
• Topological prerequisites
• Part 1 Functional analysis
• Hilbert spaces
• Banach spaces
• Locally convex spaces
• Part 2 The Lebesgue integral
• Monotone functions.- The Lebesgue integral in R
• Generalized Newton-Leibniz formula
• Integrals on measure spaces
• Part 3 Function spaces.- Spaces of continuous functions
• Spaces of integrable functions
• Almost everywhere convergence
• Hints and solutions to some exercises.- Bibliography
• Teaching remarks
• Subject index
• Name index.