Lectures on Functional Analysis and the Lebesgue Integral

Vilmos Komornik has studied in Budapest, Hungary, and has taught in Hungary and France for nearly 40 years. His main research fields are control theory of partial differential equations and combinatorial number theory. He has made a number of contributions to the theory of J.L. Lions on exact controllability and stabilization and has co-authored several papers on expansions in noninteger bases with P. Erdős.

"This book is written in a clear and readable style ... . The author gathers a collection of exercises in each chapter and presents some hints and solutions to some of them at the end of the book, helping the readers to develop their knowledge. The book is indeed a comprehensive study of Lp-spaces, useful for graduate students in mathematics, physics and engineering." (Mohammad Sal Moslehian, zbMATH 1350.46002, 2017)

• 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.