Distant future and analytic measures

Junichi Tanaka*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)799-814
Number of pages16
JournalTransactions of the American Mathematical Society
Issue number2
Publication statusPublished - 1986
Externally publishedYes


  • Analytic measures
  • Distant future
  • Quasi-invariant measures

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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