Measure Theory

J. L. Doob

ISBN 10: 0387940553 / ISBN 13: 9780387940557

Edité par Springer, Humana, 1993

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - This book was planned originally not as a work to be published, but as an excuse to buy a computer, incidentally to give me a chance to organize my own ideas ~n what measure theory every would-be analyst should learn, and to detail my approach to the subject. When it turned out that Springer-Verlag thought that the point of view in the book had general interest and offered to publish it, I was forced to try to write more clearly and search for errors. The search was productive. Readers will observe the stress on the following points. The application of pseudometric spaces. Pseudo metric, rather than metric spaces, are applied to obviate the artificial replacement of functions by equivalence classes, a replacement that makes the use of 'almost everywhere' either improper or artificial. The words 'function' and 'the set on which a function has values at least E' can be taken literally in this book. Pseudometric space properties are applied in many contexts. For example, outer measures are used to pseudometrize classes of sets and the extension of a finite measure from an algebra to a 0' algebra is thereby reduced to finding the closure of a subset of a pseudo metric space.

N° de réf. du vendeur 9780387940557

Détails bibliographiques

• Titre: Measure Theory
• Éditeur: Springer, Humana
• Date de parution: 1993
• Langue: anglais
• ISBN à 10 chiffres: 0387940553
• ISBN à 13 chiffres: 9780387940557
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 17 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 17 millimètres de profondeur
• Poids: 512 grammes

A propos de ce titre

Synopsis

This book was planned originally not as a work to be published, but as an excuse to buy a computer, incidentally to give me a chance to organize my own ideas n what measure theory every would-be analyst should learn, and to detail my approach to the subject. When it turned out that Springer-Verlag thought that the point of view in the book had general interest and offered to publish it, I was forced to try to write more clearly and search for errors. The search was productive. Readers will observe the stress on the following points. The application of pseudometric spaces. Pseudo metric, rather than metric spaces, are applied to obviate the artificial replacement of functions by equivalence classes, a replacement that makes the use of "almost everywhere" either improper or artificial. The words "function" and "the set on which a function has values at least E" can be taken literally in this book. Pseudometric space properties are applied in many contexts. For example, outer measures are used to pseudometrize classes of sets and the extension of a finite measure from an algebra to a 0" algebra is thereby reduced to finding the closure of a subset of a pseudo metric space.

Présentation de l'éditeur

This text is unique in accepting probability theory as an essential part of measure theory. Therefore, many examples are taken from probability, and probabilistic concepts such as independence and Markov processes are integrated into the text. Also, more attention than usual is paid to the role of algebras, and the metric defining the distance between sets as the measure of their symmetric difference is exploited more than is customary.