Decomposition of analytic measures on groups and measure spaces (Q2717725)

In their joint work with \textit{S. Saeki} [J. Funct. Anal. 165, 1-23 (1999; Zbl 0956.43001)], the authors introduced the notion ``sup path attaining'' and investigated properties of measures by transference methods. In particular, when \((T_t)_{t\in\mathbb{R}}\) is a sup path attaining representation of \(\mathbb{R}\) by isomorphisms of a measure space \(M(\Sigma)\), they gave a decomposition theorem of weakly analytic measures by using a theorem of Bessaga and Pełczyński concerning Banach spaces, and they derived several properties of analytic measures (F. and M. Riesz theorem, etc.). In this paper, the authors obtain similar results in the situation where \((T_t)_{t\in\mathbb{R}}\) is replaced by a sup path attaining representation of a locally compact abelian group with ordered dual.