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It is shown that there exist a probability space (X, X, ), two ergodic measure preserving transformations T, S acting on (X, X, ) with h_ (X, T) =h_ (X, S) =0, and f, g L^ (X, ) such that the limit equation* ₍1N₍=₀^N-1 f (T^nx) g (S^nx) equation* does not exist in L² (X, ).
Huang et al. (Mon,) studied this question.
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