Introduction to Measure Theory and Integration [recurso electrónico] / by Luigi Ambrosio, Giuseppe Prato, Andrea Mennucci.

Por: Ambrosio, Luigi [author.]Colaborador(es): Prato, Giuseppe [author.] | Mennucci, Andrea [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries Appunti/Lecture Notes ; 10Editor: Pisa : Edizioni della Normale, 2011Descripción: 198p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9788876423864Tema(s): Mathematics | Mathematics | Measure and IntegrationFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 515.42 Clasificación LoC:QA312-312.5Recursos en línea: Libro electrónicoTexto
Contenidos:
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.
En: Springer eBooksResumen: 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.
Star ratings
    Valoración media: 0.0 (0 votos)
Existencias
Tipo de ítem Biblioteca actual Colección Signatura Copia número Estado Fecha de vencimiento Código de barras
Libro Electrónico Biblioteca Electrónica
Colección de Libros Electrónicos QA312 -312.5 (Browse shelf(Abre debajo)) 1 No para préstamo 377431-2001

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.

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.

19

Con tecnología Koha