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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Products of quasi-measures
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by D. J. Grubb
Proc. Amer. Math. Soc. 124 (1996), 2161-2166
DOI: https://doi.org/10.1090/S0002-9939-96-03301-1
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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.
References
  • Johan F. Aarnes, Quasi-states and quasi-measures, Adv. Math. 86 (1991), no. 1, 41–67. MR 1097027, DOI 10.1016/0001-8708(91)90035-6
  • Johan F. Aarnes, Pure quasi-states and extremal quasi-measures, Math. Ann. 295 (1993), no. 4, 575–588. MR 1214949, DOI 10.1007/BF01444904
  • Aarnes, Johan, Construction of Non-Subadditive Measures and Discretization of Borel-Measures, Fund. Math. 147 (1995), 213-237.
  • Boardman, John, Quasi-measures on Completely Regular Spaces, Doctoral Dissertation, Northern Illinois University, DeKalb, IL (1994).
  • Knudsen, Finn, Topology and the Construction of Extreme Quasi-Measures, Advances in Mathematics, to appear.
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Bibliographic Information
  • D. J. Grubb
  • Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
  • Received by editor(s): October 26, 1994
  • Received by editor(s) in revised form: February 7, 1995
  • Communicated by: J. Marshall Ash
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 2161-2166
  • MSC (1991): Primary 28C05
  • DOI: https://doi.org/10.1090/S0002-9939-96-03301-1
  • MathSciNet review: 1322927