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Mesures dominées par une capacité alternée d'ordre 
Author:
A. El Kaabouchi
Journal:
Proc. Amer. Math. Soc. 121 (1994), 823-832
MSC:
Primary 28A12; Secondary 28A25, 52A99
MathSciNet review:
1189745
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Abstract: Let C be an alternating capacity of order 2 on a metrizable compact space, and let be the convex set of all measures dominated by C. We find a quite simple set of extreme elements of such that the closed convex hull of this set is . We also give other properties, including a generalization of one of Anger's results.
- [A1]
Bernd
Anger, Approximation of capacities by measures, Seminar on
Potential Theory, II, Springer, Berlin, 1971, pp. 152–170.
Lecture Notes in Math., Vol. 226. MR 0396885
(53 #745)
- [A2]
Bernd
Anger, Kapazitäten und obere Einhüllende von Massen,
Math. Ann. 199 (1972), 115–130 (German). MR 0367240
(51 #3482)
- [C]
Gustave
Choquet, Theory of capacities, Ann. Inst. Fourier, Grenoble
5 (1953–1954), 131–295 (1955). MR 0080760
(18,295g)
- [DFM]
C.
Dellacherie, D.
Feyel, and G.
Mokobodzki, Intégrales de capacités fortement
sous-additives, Seminar on Probability, XVI, Lecture Notes in Math.,
vol. 920, Springer, Berlin, 1982, pp. 8–40 (French). MR 658670
(84f:31016)
- [D]
D. Dellacherie, Appendice à l'exposé précédent, Sém. Probab. Lecture Notes Math., vol. 920, 1980-81, pp. 29-40.
- [E]
Abdelaziz
El Kaabouchi, Points extrémaux du convexe des mesures
majorées par une capacité, C. R. Acad. Sci. Paris
Sér. I Math. 313 (1991), no. 1, 37–40
(French, with English summary). MR 1115944
(92h:31008)
- [HS]
Peter
J. Huber and Volker
Strassen, Minimax tests and the Neyman-Pearson lemma for
capacities, Ann. Statist. 1 (1973), 251–263. MR 0356306
(50 #8776)
- [SP]
Lloyd
S. Shapley, Cores of convex games, Internat. J. Game Theory
1 (1971/72), 11–26; errata, ibid. 1 (1971/72), 199.
MR
0311338 (46 #10430)
- [A1]
- B. Anger, Approximation of capacities by measures, Lecture Notes in Math., vol. 226, Springer-Verlag, New York, 1971, pp. 152-170. MR 0396885 (53:745)
- [A2]
- -, Kapazitaeten und obere Einhuellende von Masson, Math. Ann. 199 (1972), 115-130. MR 0367240 (51:3482)
- [C]
- G. Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1953-54), 131-292. MR 0080760 (18:295g)
- [DFM]
- C. Dellacherie, D. Feyel, and G. Mokobodzki, Intégrale de capacités fortement sous-additives, Sém. Probab. Lecture Notes Math., vol. 920, Springer-Verlag, Berlin, Heidelberg, and New York, 1980-81, pp. 8-28. MR 658670 (84f:31016)
- [D]
- D. Dellacherie, Appendice à l'exposé précédent, Sém. Probab. Lecture Notes Math., vol. 920, 1980-81, pp. 29-40.
- [E]
- A. El Kaabouchi, Points extrémaux du convexe des mesures majorées par une capacité, C. R. Acad. Sci. Sér. I Math. 313 (1991), 37-40. MR 1115944 (92h:31008)
- [HS]
- P. J. Huber and V. Strassen, Minimax tests and the Neyman-Pearson lemma for capacities, Ann. Statist. 1 (1973), 251-263. MR 0356306 (50:8776)
- [SP]
- L. S. Shapley, Cores of convex games, Internat. J. Game Theory 1 (1971), 11-26. MR 0311338 (46:10430)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1189745-3
PII:
S 0002-9939(1994)1189745-3
Keywords:
Capacités alternées d'ordre 2
Article copyright:
© Copyright 1994 American Mathematical Society
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