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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Irreducible partitions and the construction of quasi-measures


Author: D. J. Grubb
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
Published electronically: 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 $g(X)=1$. The cohomology ring is an important tool for this investigation.


References [Enhancements On Off] (What's this?)

  • 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: https://doi.org/10.1090/S0002-9947-01-02764-7
Keywords: Quasi-measure, irreducible partition, cup product
Received by editor(s): March 3, 1998
Received by editor(s) in revised form: April 25, 2000
Published electronically: January 10, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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