The Daniell-Stone and Riesz Representation Theorems

Heinz König ()
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Heinz König: Universität des Saarlandes, Fakultät für Mathematik und Informatik

Chapter CHAPTER V in Measure and Integration, 1997, pp 143-178 from Springer

Abstract: The present chapter contains the most important consequences of the extension theories of chapter II. We shall obtain the representation theorems of Daniell-Stone and Frédéric Riesz in the spirit and scope of the extension theories. The Daniell-Stone theorem will be established in versions •=⋆στ as above, and based on inner regularity this time. The Riesz theorem will be a direct specialization of the case •=τ. It will involve all Borel-Radon measures on all Hausdorff topological spaces. We have sketched all this in the introduction. A substantial tool will be the combination of the horizontal and vertical integrals developed in sections 11 and 12.

Date: 1997
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DOI: 10.1007/978-3-540-89502-2_5

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