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Letbe an array of random variables on the probability spaceLetbe another probability measure onand, assume that under the law ofξ  is row-wise independent. Letbe the sample-divergence rate ofwith respect torelated to  ξ . A kind of strong deviation theorems, represented byof the arithmetic mean and the geometric mean of  ξ  are obtained. Moreover, no conditions are imposed on the joint distribution of  ξ .

On strong deviation theorems concerning array of dependent random sequence