Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T10:01:22.537Z Has data issue: false hasContentIssue false
  • English
  • Français

Order continuous measures

Published online by Cambridge University Press:  24 October 2008

G. T. Roberts
G. T. Roberts
Affiliation:
University of Hull
Get access Rights & Permissions [Opens in a new window]

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

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

REFERENCES

(1)Bourbaki, N.Topologie générale (Hermann; Paris, 1949).Google Scholar
(2)Kelley, J. L.General topology (Van Nostrand; New Jersey, 1955).Google Scholar
(3)McShane, E. J.Order-preserving maps and integration processes (Princeton; 1953).Google Scholar
(4)Nakano, H.Modulared semi-ordered linear spaces (Maruzen; Tokyo, 1950).Google Scholar