Geodesic
Convergence of Weighted Sums and Strong Law of Large Numbers for Convex Compact Integrable Random Sets and Fuzzy Random Sets
Journal of convex analysis, Tome 24 (2017) no. 1, pp. 213-238
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We prove several results in the a.s. convergence of weighted sums and strong law of large numbers for convex compact integrable random sets in separable Banach spaces via the norm compactness of the expectation of convex compact integrable random sets and an embedding method. The techniques are applied to prove strong law of large numbers for fuzzy random variables and other related results. Tightness conditions are discussed in comparison with earlier results in the literature.
Classification : 28B20, 60G42, 46A17, 54A20
Mots-clés : Expectation, fuzzy convex, strong law of large numbers, tight, Toeplitz sequence, weighted sum 
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     author = {N. V. Quang and H. T. Duyen},
     title = {Convergence of {Weighted} {Sums} and {Strong} {Law} of {Large} {Numbers} for {Convex} {Compact} {Integrable} {Random} {Sets} and {Fuzzy} {Random} {Sets}},
     journal = {Journal of convex analysis},
     pages = {213--238},
     year = {2017},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a15/}
}
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N. V. Quang; H. T. Duyen. Convergence of Weighted Sums and Strong Law of Large Numbers for Convex Compact Integrable Random Sets and Fuzzy Random Sets. Journal of convex analysis, Tome 24 (2017) no. 1, pp. 213-238. http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a15/