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Spaces of Quasi-Measures

Published online by Cambridge University Press:  20 November 2018

D. J. Grubb  and
Tim LaBerge
D. J. Grubb
Affiliation:
Department of Mathematical Sciences Northern Illinois University DeKalb, IL 60115 USA, email: grubb@math.niu.edu Website: http://www.math.niu.edu/∼grubb/
Tim LaBerge
Affiliation:
Department of Mathematics Centenary College Shreveport, LA 71134 USA, email: laberget@beta.centenary.edu Website: http://www.centenary.edu/∼laberget/
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Abstract

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We give a direct proof that the space of Baire quasi-measures on a completely regular space (or the space of Borel quasi-measures on a normal space) is compact Hausdorff. We show that it is possible for the space of Borel quasi-measures on a non-normal space to be non-compact. This result also provides an example of a Baire quasi-measure that has no extension to a Borel quasi-measure. Finally, we give a concise proof of the Wheeler-Shakmatov theorem, which states that if $X$ is normal and $\dim\left( X \right)\,\le \,1$, then every quasi-measure on $X$ extends to a measure.

Keywords

28C15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 3 , 01 September 1999 , pp. 291 - 297
Copyright
Copyright © Canadian Mathematical Society 1999

References

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