H-Regular Borel measures on locally compact abelian groups

Let $G$ be an LCA group, $H$ a closed subgroup, $\varGamma$ the dual group of $G$. In accordance with analogous notions in prediction theory the classes of $H$-regular and $H$-singular Borel measures on $\Gamma$ are defined. A characterization of $H$-regular measures is given and a Wold type decomposition is obtained.