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References
Arrow, K.J. and Radner, R. (1979), Allocation of resources in large teams. Econometrica 47, 361–385.
Artstein, Z. (1983), Convergence of sums of random sets. Preprint, The Weizmann Institute, to appear in Proceedings of Conference on Stochastic Geometry, Oberwolfach.
Artstein, Z. (1983), Convergence rates for the optimal values of allocation processes. Preprint, The Weizmann Institute, to appear in Math. Operations Res.
Artstein, Z. (1983), Distributions of random sets and random selections. Preprint, The Weizmann Institute, to appear in Israel J. Math.
Artstein, Z. (1983), Convexification in limit laws of random sets in Banach spaces. Preprint, The Weizmann Institute.
Artstein, Z. and Hart, S. (1981), Law of large numbers for random sets and allocation processes. Math. Operations Res. 6, 482–492.
Artstein, Z. and Vitale, R. A. (1975), A strong law of large numbers for random compact sets. Ann. of Prob. 3, 879–882.
Aumann, R. J. and Perles, M. (1965), A variational problem arising in economics. J. Math. Anal. Appl. 11, 488–503.
Billingsley, P. (1968), Convergence of Probability Measures. Wiley, New York.
Castaing, C. and Valadier, M. (1977), Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics 580, Springer-Verlag, Berlin.
Cressie, N. (1978), A strong limit theorem for random sets. Proceedings of the Conference on Spatial Patterns and Processes, Supplement to the Adv. Appl. Prob. 10, pp. 36–46.
Cressie, N. (1979), Random set limit theorems. Adv. Appl. Prob. 11, 281–282.
Cressie, N. (1979), A central limit theorem for random sets. Z. Wahrscheinlichkeitstheorie verw. Geb. 49, 37–47.
Cressie, N. (1983), Random set theory and problems of modelling. Preprint, The Flinders University of South Australia.
Gine, E., Hahn, M. G. and Zinn, J. (1983), Limit theorems for random sets: An application of probability in Banach space results. Probability in Banach Spaces IV, Lecture Notes in Mathematics 990, Springer-Verlag, Berlin, pp. 112–135.
Gine, E. and Hahn, M.G. (1983), Characterization and domains of attraction of P-stable random compact sets. Preprint, Texas A&M University.
Grenander, U. (1978), Pattern Analysis-Lectures in Pattern Theory I, Springer-Verlag, New York.
Groves, T. and Hart, S. (1982), Efficiency of resource allocation by uninformed demand. Econometrica 50, 1453–1482.
Hansen, J.C. (1983), A strong law of large numbers for random compact sets in Banach space. Preprint, University of Minnesota.
Hess, C. (1979), Theoreme ergodique el loi forte des grands nombres pour des ensembles aleatoires. C.R. Acad. Sci. Paris 288, Ser. A., 519–522.
Hiai, F. (1983), Multivalued conditional expectations, multivalued Radon-Nikodym theorems, integral representations of additive operators and multivalued strong laws of large numbers. Preprint, Science University of Tokyo.
Hildenbrand, W. (1974), Core and Equilibria of a Large Economy. Princeton University Press, Princeton, N.J.
Lyashenko, N.N. (1982), Limit theorems of independent, compact random subsets of Euclidean space. J. Soviet Math. 20, 2187–2196.
Mase, S. (1979), Random compact convex sets which are infinitely divisible with respect to Minkowski addition. Adv. Appl. Prob. 11, 834–850.
Matheron, G. (1975), Random Sets and Integral Geometry. Wiley, London.
Olech, C. (1967), Lexicographic order, range of integrals and bang-bang principle. Mathematical Theory of Control, Academic Press, New York, pp. 34–45.
Parthasarathy, K.R. (1967), Probability Measures on Metric Spaces. Academic Press, New York.
Puri, M.L. and Ralescu, D.A. (1983), Strong law of large numbers for Banach space valued random sets, Ann. of Prob. 11, 222–224.
Puri, M.L. and Ralescu, D.A. (1983), Limit theorems for random compact sets in Banach space. Preprint, Indiana University.
Rockafellar, R.T. (1976), Integral functionals, normal integrands and measurable selections. Nonlinear Operators and the Calculus of Variations, Lecture Notes in Mathematics 543, Springer-Verlag, Berlin, pp. 157–207.
Salinetti, G. (1983), Approximations for chance-constrained programming problems. Stochastics 10, 157–179.
Salinetti, G. and Wets, R. J-B. (1982), On the convergence in distribution of measurable multifunctions, normal integrands, stochastic processes and stochastic infima. Preprint, IIASA, Laxenburg.
Serra, J. (1982), Image Analysis and Mathematical Morphology. Academic Press, London.
Schurger, K. (1983), Ergodic theorems for subadditive superstationary families of convex compact random sets. Z. Wahrscheinlichkeitstheoriew verw. Geb. 62, 125–135.
Trader, D.A. and Eddy, W.F. (1981), A central limit theorem for Minkowski sums of random sets, Preprint, Carnegie-Mellon University.
Vitale, R.A. (1977), Asymptotic area and perimeter of sums of random plane convex sets. MRC Technical Report No. 1770, University of Wisconsin.
Vitale, R.A. (1981), A central limit theorem for random convex sets. Preprint, Claremont Graduate School.
Vitale, R.A. (1983), On Gaussian random sets. Preprint, Claremont Graduate School, to appear in Proceedings of Conference on Stochastic Geometry, Oberwolfach.
Vitale, R.A. (1983), Some developments in the theory of random sets. Proceedings 44th Session, Madrid, Bulletin of the International Stat. Institute, pp. 863–871.
Weil, W. (1982), An application of the central limit theorem for Banach-space-valued random variables to the theory of random sets. Z. Wahrscheinlichkeitstheorie verw. Geb. 60, 203–208.
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Artstein, Z. (1984). Limit laws for multifunctions applied to an optimization problem. In: Salinetti, G. (eds) Multifunctions and Integrands. Lecture Notes in Mathematics, vol 1091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098802
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DOI: https://doi.org/10.1007/BFb0098802
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