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ArticleOriginal scientific text

Title

A new proof of Kelley's Theorem

Authors 1

Affiliations

  1. Department of Pure Mathematics, University of Hull, Hull, HU6 7RX England

Abstract

Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.

Bibliography

  1. [F] D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebra, Vol. III, J. D. Monk and R. Bonnet (eds.), North-Holland, Amsterdam 1989, 877-980.
  2. [HL] A. Hurd and P. A. Loeb, An Introduction to Nonstandard Real Analysis, Academic Press, New York 1985.
  3. [K] J. L. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165-1177.
  4. [L] T. L. Lindstrøm, An invitation to nonstandard analysis, in: Nonstandard Analysis and its Applications, N.J. Cutland (ed.), Cambridge University Press, 1988, 1-105.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm140/fm14015.pdf

Fundamenta Mathematicae
1991-1992/140/1
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Pages:
63-67
Main language of publication
English
Received
1990-11-22
Accepted
1991-06-24
Published
1991
Exact and natural sciences