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MARC 21

Introduction to Measure Theory and Integration
Tag	Description
020	$a9788876423864
082	$a515.42
099	$aOnline Resource : Edizioni della Normale, Pisa
100	$aAmbrosio, Luigi.$d1963-
245	$aIntroduction to Measure Theory and Integration$h[Ebook]$cby Luigi Ambrosio, Giuseppe Da Prato, Andrea Mennucci.
260	$aPisa$bEdizioni della Normale$c2011
300	$a198 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aAppunti/Lecture Notes ;$v10
505	$aMeasure 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.
520	$aThis 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aDa Prato, Giuseppe$d1936-$eauthor.
700	$aMennucci, Andrea.$eauthor.
710	$aSpringerLink (Online service)
830	$aAppunti/Lecture Notes ;$v10
856	$uhttp://dx.doi.org/10.1007/978-88-7642-386-4