Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T05:47:01.124Z Has data issue: false hasContentIssue false

ON THE MARGINALS OF PROBABILITY CONTENTS ON LATTICES

Published online by Cambridge University Press:  06 February 2012

Heinz König*
Affiliation:
Fakultät für Mathematik und Informatik, Universität des Saarlandes, D-66041 Saarbrücken, Germany (email: [email protected])
Get access

Abstract

The paper extends the fundamental existence assertion for probability contents and measures with given marginals: the extension is from algebras to lattices, and thus is in accord with an actual trend in measure and integration. The proof of the basic theorem is a rapid application of a former Hahn–Banach type separation theorem.

Type
Research Article
Copyright
Copyright © University College London 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Fremlin, D. H., Measure Theory, Vol. 4, Torres Fremlin (2003), reprint 2006.Google Scholar
[2]Jacobs, K., Measure and Integral, Academic Press (New York, 1978).Google Scholar
[3]König, H., Measure and Integration, Springer (Berlin, 1997), reprint 2009.Google Scholar
[4]König, H., Upper envelopes of inner premeasures. Ann. Inst. Fourier 50(2) (2000), 401422.Google Scholar
[5]Ramachandran, D., Perfect measures and related topics. In Handbook of Measure Theory (ed. Pap, E.), Elsevier (New York, 2002), 766786.Google Scholar
[6]Strassen, V., The existence of probability measures with given marginals. Ann. Math. Statist. 36 (1965), 423439.CrossRefGoogle Scholar