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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0691275-2
Article copyright: © Copyright 1983 American Mathematical Society