Construction of non-subadditive measures and discretization of Borel measures

Johan Aarnes

Fundamenta Mathematicae (1995)

  • Volume: 147, Issue: 3, page 213-237
  • ISSN: 0016-2736

Abstract

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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 μ n , each of which only takes a finite set of values, and such that μ n converges to λ in the w*-topology.

How to cite

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Aarnes, Johan. "Construction of non-subadditive measures and discretization of Borel measures." Fundamenta Mathematicae 147.3 (1995): 213-237. <http://eudml.org/doc/212086>.

@article{Aarnes1995,
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 $μ_n$, each of which only takes a finite set of values, and such that $μ_n$ converges to λ in the w*-topology.},
author = {Aarnes, Johan},
journal = {Fundamenta Mathematicae},
keywords = {compact Hausdorff spaces; quasi-measures; regular Borel measures; solid set functions; regular non-subadditive measures},
language = {eng},
number = {3},
pages = {213-237},
title = {Construction of non-subadditive measures and discretization of Borel measures},
url = {http://eudml.org/doc/212086},
volume = {147},
year = {1995},
}

TY - JOUR
AU - Aarnes, Johan
TI - Construction of non-subadditive measures and discretization of Borel measures
JO - Fundamenta Mathematicae
PY - 1995
VL - 147
IS - 3
SP - 213
EP - 237
AB - 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 $μ_n$, each of which only takes a finite set of values, and such that $μ_n$ converges to λ in the w*-topology.
LA - eng
KW - compact Hausdorff spaces; quasi-measures; regular Borel measures; solid set functions; regular non-subadditive measures
UR - http://eudml.org/doc/212086
ER -

References

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  1. [1] J. F. Aarnes, Quasi-states and quasi-measures, Adv. in Math. 86 (1991), 41-67. Zbl0744.46052
  2. [2] J. F. Aarnes, Pure quasi-states and extremal quasi-measures, Math. Ann. 295 (1993), 575-588. Zbl0791.46028
  3. [3] C. D. Christenson and W. L. Voxman, Aspects of Topology, Dekker, New York, 1977. Zbl0347.54001
  4. [4] P. Halmos, Measure Theory, Van Nostrand, New York, 1950. 
  5. [5] F. F. Knudsen, Topology and the construction of extreme quasi-measures, Adv. in Math., to appear. Zbl0914.28010
  6. [6] H. L. Royden, Real Analysis, 2nd ed., Macmillan, New York, 1986. Zbl0197.03501

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