Integration theory / A.J.E.M. Janssen, P. van der Steen
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1078Langue : anglais.Éditeur : Berlin : Springer-Verlag, 1984ISBN: 9783540133865.ISSN: 1617-9692.Sujet MSC : 28A25, Classical measure theory, Integration with respect to measures and other set functions28-02, Research exposition (monographs, survey articles) pertaining to measure and integration
28C05, Measure and integration - Set functions and measures on spaces with additional structure, Integration theory via linear functionals representing set functions and measuresEn-ligne : Springerlink | Zentralblatt | MathSciNet
The aim of this book is to present and compare the approaches to Lebesgue integration in the circle line, that distinguishes this work from many other books. The common part of the usual methods (catch words: Carathéodory, Bourbaki, Daniel) consists of obtaining somehow a space B of basic functions on a set S, together with a positive linear functional I on B that has a certain continuity property. Then one enlarges B to a complete space L, and extends I to a positive linear functional (again denoted by I) on L. In the situation thus obtained, denoted symbolically by L(L,I) or L, one has Lebesgue’s dominated convergence theorem, which is really at the heart of any theory of integration. ... (Zentralblatt)
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