
Introduction to Measure Theory and Integration
Scuola Normale Superiore (Publisher)
Published on 22. August 2011
Book
Paperback/Softback
XIII, 187 pages
978-88-7642-385-7 (ISBN)
Description
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 of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourier series, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory.
Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra.
All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book.
Prerequisites for the book are a basic knowledge of calculus in one and several variables, metric spaces and linear algebra.
All results presented here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutions to the exercises are provided in the final part of the book.
More details
Series
Edition
1st Edition.
Language
English
Place of publication
Pisa
Switzerland
Publishing group
Birkhauser Verlag AG
Target group
College/higher education
Graduate
Illustrations
XIII, 187 p.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
454 gr
ISBN-13
978-88-7642-385-7 (9788876423857)
DOI
10.1007/978-88-7642-386-4
Schweitzer Classification
Other editions
Additional editions

Luigi Ambrosio | Giuseppe Da Prato | Andrea Mennucci
Introduction to Measure Theory and Integration
E-Book
02/2012
1st Edition
Edizioni Della Normale
€28.88
Available for download
Content
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.