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Order continuous measures

Published online by Cambridge University Press:  24 October 2008

G. T. Roberts
G. T. Roberts
Affiliation:
University of Hull
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Extract

1. Objective. It is possible to define order convergence on the vector lattice of all continuous functions of compact support on a locally compact topological space. Every measure is a linear form on this vector lattice. The object of this paper is to prove that a measure is such that every set of the first category of Baire has measure zero if and only if the measure is a linear form which is continuous in the order convergence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 2 , April 1964 , pp. 205 - 207
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

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