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Irreducible partitions and the construction of quasi-measures
Author(s):
D.
J.
Grubb
Journal:
Trans. Amer. Math. Soc.
353
(2001),
2059-2072.
MSC (2000):
Primary 28C15, 55N45, 46G12
Posted:
January 10, 2001
MathSciNet review:
1813607
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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  . The cohomology ring is an important tool for this investigation.
References:
-
- 1.
- Aarnes, Johan, Quasi-states and Quasi-measures, Advances in Mathematics 86 (1991) 41-67. MR 92d:46152
- 2.
- Aarnes, Johan, Construction of Non Subadditive Measures and Discretization of Borel Measures, Fundamenta Mathematicae 147 (1995) 213-237. MR 96k:28022
- 3.
- Jacobson, Nathan, Basic Algebra I (W. H. Freeman and Company, 1985). MR 86d:00001
- 4.
- Knudsen, Finn, Topology and the Construction of Extreme Quasi-measures, Advances in Mathematics 120 (1996), 302-321. MR 97e:28007
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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
DOI:
10.1090/S0002-9947-01-02764-7
PII:
S 0002-9947(01)02764-7
Keywords:
Quasi-measure,
irreducible partition,
cup product
Received by editor(s):
March 3, 1998
Received by editor(s) in revised form:
April 25, 2000
Posted:
January 10, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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