A certain class of total variation measures of analytic measures

Junichi Tanaka

Research output: Contribution to journalArticle

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Abstract

In this paper we investigate a problem concerning the total variation measure of an analytic measure induced by a flow. Our main results are: Let μ be a positive Baire measure on a compact Hausdorff space and let the distant future in L2(μ) be the zero subspace. If μ is absolutely continuous with respect to an invariant measure, then μ is the total variation measure of an analytic measure. On the other hand, if μ is singular with respect to each invariant measure, then there is a summable Baire function g such that gdμ is analytic and g−1 is bounded. Moreover, we note that general μ can be uniquely expressed as the sum of measures of above two types.

Original languageEnglish
Pages (from-to)547-558
Number of pages12
JournalPacific Journal of Mathematics
Volume82
Issue number2
Publication statusPublished - 1979
Externally publishedYes

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Total Variation
Invariant Measure
Compact Hausdorff Space
G-function
Absolutely Continuous
Class
Subspace
Zero

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A certain class of total variation measures of analytic measures. / Tanaka, Junichi.

In: Pacific Journal of Mathematics, Vol. 82, No. 2, 1979, p. 547-558.

Research output: Contribution to journalArticle

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