Asymptotically Brownian skew products give non-loosely BernoulliK-automorphisms
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- Rudolph, D.J. Invent Math (1988) 91: 105. doi:10.1007/BF01404914
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A quite natural exponential mixing condition on a real valued cocyclef implies that the cocycle is asymptotically approximable by Brownian motion to a degree better thant1/2. This in turn implies that the skew extension by a positive entropy ergodic flow using the cocycle is not loosely Bernoulli, in complete analogy to Kalikow'sT, T−1 argument [Kal].