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Introduction to Measure Theory and Integration
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Catalogue Information
Field name
Details
Dewey Class
515.42
Title
Introduction to Measure Theory and Integration ([Ebook]) / by Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci.
Author
Ambrosio, Luigi. , 1963-
Added Personal Name
Da Prato, Giuseppe , 1936-
Mennucci, Andrea
Other name(s)
SpringerLink (Online service)
Publication
Pisa : Edizioni della Normale , 2011
Physical Details
198 pages : online resource.
Series
Appunti/Lecture Notes
; 10
ISBN
9788876423864
Summary Note
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.:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-88-7642-386-4
Links to Related Works
Subject References:
Mathematics
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Measure and Integration
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Authors:
Ambrosio, Luigi. 1963-
.
author
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Da Prato, Giuseppe 1936-
.
Mennucci, Andrea
.
Corporate Authors:
SpringerLink (Online service)
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Series:
Appunti/Lecture Notes
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Classification:
515.42
.
515.42 (DDC 23)
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