We introduce some measures of the dependence such as the strong mixing and uniform mixing coefficients in von Neumann algebras and then define the noncommutative strong and uniform mixing sequences. We establish some notable nonncommutative mixing inequalities such as Ibragimov inequality. Moreover, we extend the notion of mixingale sequence to the noncommutative content and demonstrate a noncommutative L1 and weak law of large numbers for uniformly integrable L1-mixingale sequences. In addition, we investigate the noncommutative Lp-near-epoch dependence and provide some conditions under which a noncommtative Lp-near-epoch dependent sequence is a noncommutative Lp-mixingale. Finally, we introduce the concept of noncommutative Lp-approximability and show that in the setting of quantum (noncommutative) probability spaces, an Lr-bounded and L0-approximable sequence is Lp-approximable for 1≤p and 2p

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