Admissible transformations of measures - Gabriyelyan, S. S. (Журнал математичної фізики, аналізу, геометрії, 2005)
Let a topological semigroup G acts on a topological space X. A transformation gG is called an admissible (partially admissible, singular, equivalent, invariant) transform for μ relative to u if μ_gu (accordingly: μ_g otu, μ_gu, μ_gu, μ_g=c· u), where μ_g(E):=μ(g^-1E). We denote its collection by A(μ\!\!\!\! u) (accordingly: AP(μ\!\!\!\! u), S(μ\!\!\!\! u), E(μ\!\!\!\! u), I(μ\!\!\!\! u)). The algebraic and the measure theoretical properties of these sets are studied. It is done the Lebesgue-type decomposition. If G=X is a locally compact group, we give some informations about the measure theoretical size of A(μ). Mathematical Subject Classification: 28C99, 37A99.