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.
