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Journal of Convex Analysis 24 (2017), No. 1, 213--238
Copyright Heldermann Verlag 2017

Convergence of Weighted Sums and Strong Law of Large Numbers for Convex Compact Integrable Random Sets and Fuzzy Random Sets

Nguyen Van Quang
Vinh University, Nghe An Province, Vietnam

Hoang Thi Duyen
Quang Binh University, Quang Binh Province, Vietnam

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.

Keywords: Expectation, fuzzy convex, strong law of large numbers, tight, Toeplitz sequence, weighted sum.

MSC: 28B20, 60G42, 46A17, 54A20

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