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Central limit theorem for Banach space valued fuzzy random variables


Authors: Frank N. Proske and Madan L. Puri
Journal: Proc. Amer. Math. Soc. 130 (2002), 1493-1501
MSC (2000): Primary 60F05; Secondary 46B09
DOI: https://doi.org/10.1090/S0002-9939-01-06208-6
Published electronically: October 23, 2001
MathSciNet review: 1879975
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Abstract: In this paper we prove a central limit theorem for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.


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  • 1. Z. Artstein and R.A. Vitale, A strong law of large numbers for random compact sets, Ann. Prob. 3 (1975), 879-882. MR 52:6825
  • 2. J.P. Aubin and H. Frankowska, Set-valued Analysis. Systems and Control: Foundations and Applications, Birkhäuser, 1990. MR 91d:49001
  • 3. L. Breiman, Probability. Addison-Wesley, 1968. MR 37:4841
  • 4. G. Debreu, Integration of correspondences, Proc. Fifth Berkeley Symp. Math Statist. Prob. 2 (1966), 351-372, University of California Press. MR 37:3835
  • 5. N. Dunford and J.T. Schwartz, Linear Operators, Part I. Interscience, 1958. MR 22:8302
  • 6. E. Giné, M.G. Hahn and J. Zinn, Limit theorems for random sets, Springer Lecture Notes in Math. 990 (1983), 112-135. MR 85d:60019
  • 7. L. Hörmander, Sur la fonction d`appui des ensembles convexe dans un espace localement convexe, Ark. Mat. 3 (1954), 181-186. MR 16:831e
  • 8. E.P. Klement, M.L. Puri and D.A. Ralescu, Limit theorems for fuzzy random variables, Proc. Royal Soc. Lond. A 407 (1986), 171-182.MR 88b:60092
  • 9. F.N. Proske, Limit theorems for fuzzy random variables, Ph.D. Thesis, Ulm University, Germany, 1997.
  • 10. M.L. Puri and D.A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl. 91 (1983), 552-558. MR 85c:26014
  • 11. M.L. Puri and D.A. Ralescu, Limit theorems for random compact sets in Banach spaces, Math. Proc. Cam. Phil. Soc. 97 (1985), 151-158. MR 86c:60024
  • 12. M.L. Puri and D.A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986), 409-422. MR 87f:03159
  • 13. A.W. van der Vaart and J.A. Wellner, Weak convergence and empirical processes, Springer, 1996. MR 97g:60035
  • 14. W. Weil, An application of the central limit theorem for Banach space valued random variables to the theory of random sets, Z. Wahrscheinlichkeitstheor. Verw. Geb. 60 (1982), 203-208. MR 83h:60010
  • 15. L.A. Zadeh, Fuzzy Sets, Information and Control 8 (1965), 338-353.MR 36:2509

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Additional Information

Frank N. Proske
Affiliation: Abt. Math. III, Universität Ulm, 89069 Ulm, Germany
Address at time of publication: Department of Mathematics, University of Oslo, 1053 Blindern, 0316 Oslo, Norway
Email: frproske@metronet.de, proske@math.uio.no

Madan L. Puri
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: puri@indiana.edu

DOI: https://doi.org/10.1090/S0002-9939-01-06208-6
Received by editor(s): May 20, 2000
Received by editor(s) in revised form: November 22, 2000
Published electronically: October 23, 2001
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2001 American Mathematical Society

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