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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Additional Information

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