Elements of mathematics - Integration I

Chapters 1-6

Pierre Samuel

472 pages, parution le 28/11/2003

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Résumé

To the reader

The Elements of Mathematics series takes up mathematics at their beginning, and gives complete proofs. In principle, it requires no particular knowledge of mathematics on the reader's part, but only a certain familiarity with mathematical reasoning and a certain capacity for abstract thought. Nevertheless, it is directed especially to those who have a good knowledge of at least the content of the first year or two of a university mathematics course.

The method of exposition we have chosen is axiomatic, and normally proceeds from the general to the particular. The; demands of proof impose a rigorously fixed order on the subject matter. It follows that the utility of certain considerations will not be immediately apparent to the reader unless lie already has a fairly extensive knowledge of mathematics.

The series is divided into Books, and each Book into chapters. The Books already published, either in whole or in part, in the French edition, are listed below. When an English translation is available, the corresponding English title is mentioned between parentheses. Throughout the volume a reference indicates the English edition, when available, and the French edition otherwise.

Introduction
Inequalities Of Convexity
- The fundamental inequality of convexity
- The inequalities of Holder and Minkowski
- The semi-norms Np
Riesz Spaces
- Riesz spaces and fully lattice-ordered spaces
- Linear forms on a Riesz space
Measures on locally compact spaces
- Measures on a locally compact space
- Support of a measure
- Integrals of continuous vector-valued functions
- Products of measures
Extension of a measure. Lp spaces
- Upper integral of a positive function
- Negligible functions and sets
- Lp spaces
- Integrable functions and sets
- Measurable functions and sets
- Convexity inequalities
- Barycenters
Integration of measures
- Essential upper integral
- Summable families of positive measures
- Integration of positive measures
- Integration of positive point measures
- Measures defined by numerical densities
- Images of a measure
- Integration with respect to an induced measure
- Products of measures
Vectorial integration
- Integration of vector-valued functions
- Vectorial measures
- Disintegration of measures

L'auteur - Pierre Samuel

Pierre Samuel, spécialiste d'algèbre et de géométrie algébrique, est professeur à l'Université de Paris-Sud (Orsay).

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Pierre Samuel
Parution	28/11/2003
Nb. de pages	472
Format	16 x 24
Couverture	Relié
Poids	835g
Intérieur	Noir et Blanc
EAN13	9783540411291