On the convergence of closed-valued measurable multifunctions
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- by Gabriella Salinetti and Roger J.-B. Wets PDF
- Trans. Amer. Math. Soc. 266 (1981), 275-289 Request permission
Abstract:
In this paper we study the convergence almost everywhere and in measure of sequences of closed-valued multifunctions. We first give a number of criteria for the convergence of sequences of closed subsets. These results are used to obtain various characterizations for the convergence of measurable multifunctions. In particular we are interested in the convergence properties of (measurable) selections.References
- C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, Vol. 580, Springer-Verlag, Berlin-New York, 1977. MR 0467310, DOI 10.1007/BFb0087685
- R. Tyrrell Rockafellar, Integral functionals, normal integrands and measurable selections, Nonlinear operators and the calculus of variations (Summer School, Univ. Libre Bruxelles, Brussels, 1975) Lecture Notes in Math., Vol. 543, Springer, Berlin, 1976, pp. 157–207. MR 0512209
- G. Choquet, Convergences, Ann. Univ. Grenoble. Sect. Sci. Math. Phys. (N.S.) 23 (1948), 57–112. MR 0025716
- Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182. MR 42109, DOI 10.1090/S0002-9947-1951-0042109-4
- D. W. Curtis and R. M. Schori, $2^{x}$ and $C(X)$ are homeomorphic to the Hilbert cube, Bull. Amer. Math. Soc. 80 (1974), 927–931. MR 353235, DOI 10.1090/S0002-9904-1974-13579-2
- Gerard Debreu, Integration of correspondences, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Univ. California Press, Berkeley, Calif., 1967, pp. 351–372. MR 0228252
- J. Neveu, Convergence presque sûre de martingales multivoques, Ann. Inst. H. Poincaré Sect. B (N.S.) 8 (1972), 1–7 (French, with English summary). MR 0331504
- G. Matheron, Random sets and integral geometry, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York-London-Sydney, 1975. With a foreword by Geoffrey S. Watson. MR 0385969
- Gabriella Salinetti and Roger J.-B. Wets, On the convergence of sequences of convex sets in finite dimensions, SIAM Rev. 21 (1979), no. 1, 18–33. MR 516381, DOI 10.1137/1021002
- Maurice Sion, A theory of semigroup valued measures, Lecture Notes in Mathematics, Vol. 355, Springer-Verlag, Berlin-New York, 1973. MR 0450503, DOI 10.1007/BFb0060133
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 266 (1981), 275-289
- MSC: Primary 28A20; Secondary 54C60
- DOI: https://doi.org/10.1090/S0002-9947-1981-0613796-3
- MathSciNet review: 613796