### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Pacific Journal of Mathematics*,

*82*(2), 547-558.

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

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 82, no. 2, pp. 547-558.

}

TY - JOUR

T1 - A certain class of total variation measures of analytic measures

AU - Tanaka, Junichi

PY - 1979

Y1 - 1979

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84972568460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972568460&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84972568460

VL - 82

SP - 547

EP - 558

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -