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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Distant future and analytic measures


Author: Jun-ichi Tanaka
Journal: Trans. Amer. Math. Soc. 296 (1986), 799-814
MSC: Primary 28D05; Secondary 43A17
DOI: https://doi.org/10.1090/S0002-9947-1986-0846607-6
MathSciNet review: 846607
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Abstract: Using a representation of analytic measures in terms of a flow built under a function, it is shown that a positive measure is the total variation measure of an analytic measure if and only if the distant future is the zero subspace. This settles a problem posed by Forelli in connection with his generalization of F. and M. Riesz theorems. We also provide another version of Helson's existence theorem.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0846607-6
Keywords: Analytic measures, quasi-invariant measures, distant future
Article copyright: © Copyright 1986 American Mathematical Society