Description

The choice of topics included in this book, as well as the presentation of those topics, has been guided by the author’s experience in teaching this material to classes consisting of advanced graduate students who are not concentrating in mathematics. This book contains an introduction to the modern theory of integration with a strong emphasis on the case of LEBESGUE’s measure for (RN and eye toward applications to real analysis and probability theory. Following a brief review of the classical RIEMANN theory in Chapter I, the details of LEBESGUE’s construction are given in Chapter II, which also contains a derivation of the transformation properties of LEBESGUE’s measure under linear maps. Chapter III is devoted to LEBESGUE’s theory of integration of real-valued functions on a general measure space. Besides the basic convergence theorems, this chapter introduces product measures and FUBINI’s Theorem. In Chapter IV, various topics having to do with the transformation properties of measures are derived. These include: the representation of general integrals in terms of RIEMANN integrals with respect to the distribution function, polar coordinates, JACOBI’s transformation formula and finally the introduction of surface measure followed by a proof of the Divergence Theorem. A few of the basic inequalitites of measure theory are derived in Chapter V. In particular, the inequalities of JENSEN, MINKOWSKI and HOELDER are presented. Finally, Chapter VI starts with the DANIELL integral and its applications to the CARATHEODORY Extension and RIESZ Representation Theorems. It closes with VON NEUMANN’s derivation of the RADON-NIKODYM Theorem.

Langue

en

Version

Couverture rigide

Date de sortie initiale

01 mars 1990

Nombre de pages

160

Illustrations

Non

Personnes impliquées

Auteur principal

Daniel W Stroock

Deuxième auteur

Daniel W. Stroock

Editeur principal

World Scientific Publishing Co Pte Ltd

Informations sur le fabricant

Nom du fabricant

Libri GmbH

Adresse électronique du fabricant

[email protected]

Informations sur le fabricant

Les informations du fabricant ne sont actuellement pas disponibles

Autres spécifications

Hauteur de l’emballage

17 mm

Largeur d’emballage

162 mm

Livre d‘étude

Oui

Longueur d’emballage

232 mm

Poids de l’emballage

374 g

Police de caractères extra large

Non

EAN

EAN

9789810201456

Sécurité des produits

Opérateur économique responsable dans l’UE

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Catégories

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Disponibilité

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Langue

Anglais

Type de livre

Hardcover