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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Additivity of quasi-measures


Authors: D. J. Grubb and Tim LaBerge
Journal: Proc. Amer. Math. Soc. 126 (1998), 3007-3012
MSC (1991): Primary 28C15
DOI: https://doi.org/10.1090/S0002-9939-98-04494-3
MathSciNet review: 1458874
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Abstract: We prove that quasi-measures on compact Hausdorff spaces are countably additive. Contained in this result is a proof that every quasi-measure decomposes uniquely into a measure and a quasi-measure that has no smaller measure beneath it. We also show that it is consistent with the usual axioms of set-theory that quasi-measures on compact Hausdorff spaces are $\aleph _1$-additive. Finally, we construct an example that places strong restrictions on other forms of additivity.


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Additional Information

D. J. Grubb
Affiliation: Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115
Email: grubb@math.niu.edu

Tim LaBerge
Affiliation: Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115
Email: laberget@math.niu.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04494-3
Received by editor(s): December 23, 1996
Received by editor(s) in revised form: March 13, 1997
Communicated by: Dale E. Alspach
Article copyright: © Copyright 1998 American Mathematical Society