Optimal approximations of capacities on a metric compactum (in Ukrainian)

I.D.Hlushak

For a capacity on a metric compactum an optimal approximation by a $\cup$-capacity (or by a $\cap$-capacity) w.r.t. a Prohorov-style metric is constructed. A method is also presented for optimal approximation of a capacity on a metric compactum by a capacity on a fixed closed subspace.

1. G.~Choquet, Theory of Capacity, Ann. Inst. Fourier (Grenoble), 5 (1953-1954) 131--295.

2. L.~Epstein, T.~Wang, ``Beliefs about beliefs'' without probabilities, Econometrica, 64 (1996) №5, 1343--1373.

3. D.~Schmeidler, Subjective Probability and Expected Utility without Additivity, Econometrica, 57 (1989) 571--587.

4. Zhou Lin, Integral representation of continuous comonotonically additive functionals, Trans. Amer. Math. Soc. 350 (1998) №5, 1811--1822.

5. G.L.~O'Brien, W.~Verwaat, How subsadditive are subadditive capacities? Comment. Math. Univ. Carolin. 35 (1994) №2, 311--324.

6. M.M.~Zarichnyi, O.R.~Nykyforchyn, Capacity functor in the category of compacta, Mat. Sb. 199 (2008) №2, 3--26.

7. I.D.~Hlushak, O.R.~Nykyforchyn, Submonads of the capacity monad, Carpathian J. Math. 24 (2008) №1, 56--67.

	Optimal approximations of capacities on a metric compactum (in Ukrainian)
Author	I.D.Hlushak Vasyl Stefanyk Precarpathian National University, Faculty of Mathematics and Informatics, 57 Shevchenka street, Ivano-Frankivsk, Ukraine
Abstract	For a capacity on a metric compactum an optimal approximation by a $\cup$-capacity (or by a $\cap$-capacity) w.r.t. a Prohorov-style metric is constructed. A method is also presented for optimal approximation of a capacity on a metric compactum by a capacity on a fixed closed subspace.
Keywords	capacity, metric compactum, optimal approximation
DOI	doi:10.30970/ms.31.2.115-121
Reference	1. G.~Choquet, Theory of Capacity, Ann. Inst. Fourier (Grenoble), 5 (1953-1954) 131--295. 2. L.~Epstein, T.~Wang, ``Beliefs about beliefs'' without probabilities, Econometrica, 64 (1996) №5, 1343--1373. 3. D.~Schmeidler, Subjective Probability and Expected Utility without Additivity, Econometrica, 57 (1989) 571--587. 4. Zhou Lin, Integral representation of continuous comonotonically additive functionals, Trans. Amer. Math. Soc. 350 (1998) №5, 1811--1822. 5. G.L.~O'Brien, W.~Verwaat, How subsadditive are subadditive capacities? Comment. Math. Univ. Carolin. 35 (1994) №2, 311--324. 6. M.M.~Zarichnyi, O.R.~Nykyforchyn, Capacity functor in the category of compacta, Mat. Sb. 199 (2008) №2, 3--26. 7. I.D.~Hlushak, O.R.~Nykyforchyn, Submonads of the capacity monad, Carpathian J. Math. 24 (2008) №1, 56--67.
Pages	115-121
Volume	31
Issue	2
Year	2009
Journal	Matematychni Studii
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