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ArticleOriginal scientific text

Title

Construction of non-subadditive measures and discretization of Borel measures

Authors 1

Affiliations

  1. University of Trondheim, AVH, Department of Mathematics and Statistics, 7055 Dragvoll, Norway

Abstract

The main result of the paper provides a method for construction of regular non-subadditive measures in compact Hausdorff spaces. This result is followed by several examples. In the last section it is shown that "discretization" of ordinary measures is possible in the following sense. Given a positive regular Borel measure λ, one may construct a sequence of non-subadditive measures μn, each of which only takes a finite set of values, and such that μn converges to λ in the w*-topology.

Bibliography

  1. J. F. Aarnes, Quasi-states and quasi-measures, Adv. in Math. 86 (1991), 41-67.
  2. J. F. Aarnes, Pure quasi-states and extremal quasi-measures, Math. Ann. 295 (1993), 575-588.
  3. C. D. Christenson and W. L. Voxman, Aspects of Topology, Dekker, New York, 1977.
  4. P. Halmos, Measure Theory, Van Nostrand, New York, 1950.
  5. F. F. Knudsen, Topology and the construction of extreme quasi-measures, Adv. in Math., to appear.
  6. H. L. Royden, Real Analysis, 2nd ed., Macmillan, New York, 1986.

Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm147/fm14732.pdf

Fundamenta Mathematicae
1995/147/3
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Pages:
213-237
Main language of publication
English
Received
1994-01-28
Accepted
1995-01-27
Published
1995
Exact and natural sciences