# Construction of non-subadditive measures and discretization of Borel measures

Fundamenta Mathematicae (1995)

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

## Access Full Article

top## Abstract

top## How to cite

topAarnes, 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

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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.