Neuware -This collection of Heinz K�nig�s publications connects to his book of 1997 �Measure and Integration� and presents significant developments in the subject from then up to the present day. The result is a consistent new version of measure theory, including selected applications. The basic step is the introduction of the inner � (bullet) and outer � (bullet) premeasures and their extension to unique maximal measures. New �envelopes� for the initial set function (to replace the traditional Carath�odory outer measures) have been created, which lead to much simpler and more explicit treatment. In view of these new concepts, the main results are unmatched in scope and plainness, as well as in explicitness. Important examples are the formation of products, a unified Daniell-Stone-Riesz representation theorem, and projective limits.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 528 pp. Englisch.

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Detalles bibliogr�ficos

T�tulo: Measure and Integration
Editor: Springer Basel, Birkh�user Basel Jun 2012
Fecha de publicaci�n: 2012
Idioma: Ingl�s
ISBN 10: 3034803818
ISBN 13: 9783034803816
Encuadernaci�n: Buch
Estado: Neu

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Sinopsis

This collection of Heinz K�nig's publications connects to his book of 1997 "Measure and Integration" and presents significant developments in the subject from then up to the present day. The result is a consistent new version of measure theory, including selected applications. The basic step is the introduction of the inner • (bullet) and outer • (bullet) premeasures and their extension to unique maximal measures. New "envelopes" for the initial set function (to replace the traditional Carath�odory outer measures) have been created, which lead to much simpler and more explicit treatment. In view of these new concepts, the main results are unmatched in scope and plainness, as well as in explicitness. Important examples are the formation of products, a unified Daniell-Stone-Riesz representation theorem, and projective limits.

Further to the contributions in this volume, after 2011 Heinz K�nig published two more articles that round up his work: On the marginals of probability contents on lattices (Mathematika 58, No. 2, 319-323, 2012), and Measure and integration: the basic extension and representation theorems in terms of new inner and outer envelopes (Indag. Math., New Ser. 25, No. 2, 305-314, 2014).

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Heinz K�nig is a distinguished analyst, who has given lasting contributions to functional analysis, distribution theory, convex analysis, mathematical economics and many other fields of mathematics. Typical of his work is the analysis or creation of basic new concepts from most original viewpoints. Heinz K�nig gave a large number of original, short and elegant proofs of fundamental results in mathematics. Most remarkable is the new theory of measure and integration he developed in the last two decades.

Born in Stettin (Szczecin/Poland), Heinz K�nig has been a professor at the University of Saarland (Germany) since 1965 and a visiting professor at many prestigious universities around the world.

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