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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Products of quasi-measures


Author: D. J. Grubb
Journal: Proc. Amer. Math. Soc. 124 (1996), 2161-2166
MSC (1991): Primary 28C05
MathSciNet review: 1322927
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Abstract: A quasi-state is a positive functional on $C(X)$ that is only assumed to be linear on singly-generated subalgebras. We consider the ``iterated integral'' of two quasi-states and determine when this gives a quasi-state on the product space. We also provide explicit formulas for the corresponding quasi-measures in case it does. Finally, we show the general failure of Fubini's Theorem for quasi-states.


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Additional Information

D. J. Grubb
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03301-1
PII: S 0002-9939(96)03301-1
Received by editor(s): October 26, 1994
Received by editor(s) in revised form: February 7, 1995
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society