Vol. 82, No. 2, 1979

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A certain class of total variation measures of analytic measures

Jun-ichi Tanaka

Vol. 82 (1979), No. 2, 547–558

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 g1 is bounded. Moreover, we note that general μ can be uniquely expressed as the sum of measures of above two types.

Mathematical Subject Classification 2000
Primary: 28C15
Received: 13 April 1978
Published: 1 June 1979
Jun-ichi Tanaka