Some remarks on simply invariant subspaces on compact abelian groups

Jun-ichi TANAKA
1978 Journal of the Mathematical Society of Japan  
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
more » ... e 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. X n (Eu) = = \ 1 lL E {x + s + u)ds \dμ n (x)
doi:10.2969/jmsj/03030475 fatcat:txxb5tdf4rfgfg4kj7xe4wjigy