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Let be a non-autonomous discrete system and  be a set-valued discrete system induced by it. Where, is the space formed by all non-empty compact subsets of X endowed with the Hausdorff metric H, is a set-valued mapping sequence induced by . It is proved that  is -chaos, then  is -chaos. Where -chaos is denoted to -sensitive, -sensitive, -transitive, -accessible, -weakly mixing, -m-sensitive, infinitely sensitive, or syndetically transitive.

Chaotic Properties in the Sense of Furstenberg Families in Set-Valued Discrete Dynamical Systems