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We deduce sufficient conditions for the Central Limit Theorem (CLT) in theLebesgue-Riesz space L(p) defined on some measure space for the sequence ofcentered random variables satisfying the strong mixing (Rosenblatt) condition.  We investigate the asymptotical as well as non-asymptotical approach.

Central Limit Theorem in Lebesgue-Riesz spaces for weakly dependent random sequences