Irreducible partitions and the construction of quasi-measures
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- by D. J. Grubb PDF
- Trans. Amer. Math. Soc. 353 (2001), 2059-2072 Request permission
Abstract:
A quasi-measure is a non-subadditive measure defined on only open or closed subsets of a compact Hausdorf space. We investigate the nature of irreducible partitions as defined by Aarnes and use the results to construct quasi-measures when $g(X)=1$. The cohomology ring is an important tool for this investigation.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, Construction of non-subadditive measures and discretization of Borel measures, Fund. Math. 147 (1995), no. 3, 213–237. MR 1348720, DOI 10.4064/fm-147-3-213-237
- Nathan Jacobson, Basic algebra. I, 2nd ed., W. H. Freeman and Company, New York, 1985. MR 780184
- Finn F. Knudsen, Topology and the construction of extreme quasi-measures, Adv. Math. 120 (1996), no. 2, 302–321. MR 1397085, DOI 10.1006/aima.1996.0041
Additional Information
- D. J. Grubb
- Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
- Email: grubb@math.niu.edu
- Received by editor(s): March 3, 1998
- Received by editor(s) in revised form: April 25, 2000
- Published electronically: January 10, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 2059-2072
- MSC (2000): Primary 28C15, 55N45, 46G12
- DOI: https://doi.org/10.1090/S0002-9947-01-02764-7
- MathSciNet review: 1813607