Construction of non-subadditive measures and discretization of Borel measures

• Autorzy: Johan F. Aarnes
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1995
• Tom: 147
• Numer: 3
• Strony: 213-237

Daty

wydano

1995

otrzymano

1994-01-28

poprawiono

1995-01-27

Twórcy

autor

Johan F. Aarnes

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

Bibliografia

• [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.