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Another proof of the existence of the ergodic Hilbert transform

Author: Karl Petersen
Journal: Proc. Amer. Math. Soc. 88 (1983), 39-43
MSC: Primary 28D05; Secondary 42A50
MathSciNet review: 691275
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Abstract: We give a direct proof of the existence of the ergodic Hilbert transform $ \sum _{k = - \infty }^{\infty '}f({T^k}x)/k$, where $ T:X \to X$ is a measure-preserving transformation and $ f$ is an integrable function.

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