### 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 L^{2}(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 language | English |
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Pages (from-to) | 547-558 |

Number of pages | 12 |

Journal | Pacific Journal of Mathematics |

Volume | 82 |

Issue number | 2 |

Publication status | Published - 1979 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Tanaka, J. (1979). A certain class of total variation measures of analytic measures.

*Pacific Journal of Mathematics*,*82*(2), 547-558.