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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[A1] [A1] Aarnes, J., Quasi-states and quasi-measures. Adv.Math. 86 (1991), 41–67. Google Scholar

[A2] [A2] Aarnes, J., Pure quasi-states and extremal quasi-measures. Math. Ann. 295 (1993), 575–588. Google Scholar

[A3] [A3] Aarnes, J., Construction of non-subadditive measures and discretization of Borel measures. Fund. Math. 147 (1995), 213–237. Google Scholar

[BS] [BS] Bachman, G. and Sultan, A., On regular extensions of measures. Pacific J. Math. 86 (1980), 389–395. Google Scholar

[B1] [B1] Boardman, J., Quasi-measures on completely regular spaces. Doctoral dissertation, Northern Illinois University, 1994. Google Scholar

[B2] [B2] Boardman, J., Quasi-measures on completely regular spaces. Rocky Mountain J. Math. (2) 27 (1997), 447–470. Google Scholar

[F] [F] Fremlin, D., On quasi-measures. Preprint. Google Scholar

[S] [S] Shakmatov, D., Linearity of quasi-states on commutative C*-algebras of stable rank 1. Preprint. Google Scholar

[T] [T] Topsoe, F., Compactness in spaces of measures. Studia Math. 36 (1970), 195–212. Google Scholar

[W] [W] Wheeler, R. F., Quasi-measures and dimension theory. Topology Appl. 66 (1995), 75–92. Google Scholar

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