Another proof of the existence of the ergodic Hilbert transform

Petersen, Karl

doi:10.1090/S0002-9939-1983-0691275-2

Another proof of the existence of the ergodic Hilbert transform
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by Karl Petersen

Proc. Amer. Math. Soc. 88 (1983), 39-43

DOI: https://doi.org/10.1090/S0002-9939-1983-0691275-2

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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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