On Chung's type law of large numbers for fuzzy random variables

Abstract

Let { X n | n ⩾ 1 } be a sequence of independent fuzzy random variables and { a n | n ⩾ 1 } a sequence of positive real numbers converging to ∞ . In this paper we show that, under the assumption ∑ n = 1 ∞ E φ ( ∥ X n ∥ ρ p ) / φ ( a n ) < ∞ with some restrictions on φ , S n / a n → 0 ˜ a.s. if and only if S n / a n → 0 ˜ in probability if and only if S n / a n → 0 ˜ in L 1 where S n = ∑ i = 1 n X i . This will generalize earlier results of strong law of large numbers for random elements in a Banach space (Choi and Sung (1988). Bull. Austral. Math. Soc. 37, 93–100).