Real Analysis and Probability - Couverture souple

Livre 20 sur 151: Cambridge Studies in Advanced Mathematics

Dudley, R. M.

 
9780521007542: Real Analysis and Probability
Couverture souple
ISBN 10 : 0521007542 ISBN 13 : 9780521007542
Editeur : Cambridge University Press, 2002

Synopsis

This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Revue de presse

'A marvellous work which will soon become a standard text in the field for both teaching and reference ... a complete and pedagogically perfect presentation of both the necessary preparatory material of real analysis and the proofs throughout the text. Some of the topics and proofs are rarely found in other textbooks.' Proceedings of the Edinburgh Mathematical Society

'Careful, scholarly, and stimulating. It would be a pleasure to teach a mathematically-oriented graduate-level course from this text.' Short Book Reviews of the ISI

'[It] will serve for a long time as a standard reference.' Zentralblatt fur und ihre Grenzgebiete

'What makes the book special ... is the care and scholarship with which the material is treated, and the choice of additional topics ... not usually covered in first year graduate courses.' Mathematical Reviews

'The book serves as a clear, rigorous, and complete introduction to modern probability theory using methods of mathematical analysis, and a description of relations between the two fields ... it could be very useful for students interested in learning both topics, it can also serve as complementary reading to standard lectures. Teachers preparing their graduate level courses can use the book as an excellent, rigorously written and complete source.' EMS Newsletter

Présentation de l'éditeur

This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2002
Langue
anglais
ISBN 10 
0521007542
ISBN 13 
9780521007542
Reliure
Broché
Numéro d'édition
2
Nombre de pages
568
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

chemin des peupliers 27
Dardilly
France

Autres éditions populaires du même titre

9780521809726: Real Analysis and Probability

Edition présentée

ISBN 10 :  052180972X ISBN 13 :  9780521809726
Editeur : Cambridge University Press, 2002
Couverture rigide