A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

Proceedings of the American Mathematical Society

Volumn 131, Issue 9, 2003, Pages 2937-2944

  Proske, Frank N ^a,b   Puri, Madan L ^c  

^a UNIVERSITY OF ULM   (Germany)

^b UNIVERSITY OF OSLO   (Norway)

^c INDIANA UNIVERSITY   (United States)

Author keywords

Embedding; Empirical process; Fuzzy random variable; Fuzzy set; Hausdorff distance; Random set; Strong law of large numbers

Indexed keywords

EID: 0041351880     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-03-06842-4     Document Type: Conference Paper

References (16)

1. Artstein, Z. and Vitale, R.A. (1975). A strong law of large numbers for random compact sets. Ann. Prob. 3, 879-882. MR 52:6825
2. Aubin, J.P, and Frankowska, H. (1990). Set-valued Analysis. Systems & Control: Foundations & Applications, Birkhäuser. MR 91d:49001
3. Chow, Y.S. and Teicher, H. (1978). Probability theory. Springer. MR 80a:60004
4. Debreu, G. (1966). Integration of correspondences. Proc. Fifth Berkeley Symp. Math. Statist. Prob. 2, 351-372, University of California Press. MR 37:3835
5. Etemadi, N. (1981). An elementary proof of the strong law of large numbers. Z. Wahrscheinlichkeitstheor. Verw. Geb. 55, 119-122. MR 82b:60027
6. Giné, E., Hahn, G. and Zinn, J. (1983). Limit theorems for random sets. Springer Lecture notes in Math. 990, 112-135. MR 85d:60019
7. Hoffmann-Jørgensen, J. (1985). The law of large numbers for non-measurable and non-separable random elements. Colloque en l'honneur de L. Schwartz, pp. 299-356, Astérisque Vol. 131. Hermann, Paris 1985. MR 88a:60014
8. Klement, E.P., Puri, M.L. and Ralescu, D.A. (1986). Limit theorems for fuzzy random variables, Proc. R. Soc. Lond. A 407, 171-182. MR 88b:60092
9. Kruse, R. (1982). The strong law of large numbers for fuzzy random variables. Inform. Sci. 28, 233-241. MR 84k:60046
10. Proske, F.N. (1997). Limit theorems for fuzzy random variables. Ph.D. Thesis, Ulm University, Germany.
11. Proske, F.N. and Puri, M.L. (2002). Central Limit Theorem for Banach Space valued fuzzy random variables. Proc. Amer. Math. Soc. 130, 1493-1501.
12. Puri, M.L. and Ralescu, D.A. (1983). Differentials of fuzzy functions, J. Math. Anal. Appl. 91, 552-558. MR 85c:26014
13. _ (1985). Limit theorems for random compact sets in Banach spaces, Math. Proc. Cam. Phil. Soc. 97, 151-158. MR 86c:60024
14. _ (1986). Fuzzy random variables. J. Math. Anal. Appl. 114, 409-422. MR 87f:03159
15. Talagrand, M. (1987). The Glivenko-Cantelli problem. Ann. Prob. 15, 837-870. MR 88h:60012
16. Zadeh, L.A. (1965). Fuzzy Sets, Information and Control 8, 338-353. MR 36:2509