Geodesic
Spaces of Quasi-Measures
Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 291-297

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DOI

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.
DOI : 10.4153/CMB-1999-035-5
Mots-clés : 28C15 
Grubb, D. J.; LaBerge, Tim. Spaces of Quasi-Measures. Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 291-297. doi: 10.4153/CMB-1999-035-5
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     title = {Spaces of {Quasi-Measures}},
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     year = {1999},
     volume = {42},
     number = {3},
     doi = {10.4153/CMB-1999-035-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-035-5/}
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