Let a topological semigroup G acts on a topological space X. A transformation g∈G is called an admissible (partially admissible, singular, equivalent, invariant) transform for μ relative to ν if μg≪ν (accordingly: μg⊥̸ν, μg⊥ν, μg∼ν, μg=c⋅ν), where μg(E):=μ(g−1E). We denote its collection by A(μ|ν) (accordingly: AP(μ|ν), S(μ|ν), E(μ|ν), I(μ|ν)). 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).
|Number of pages||27|
|Journal||Journal of Mathematical Physics, Analysis, Geometry|
|State||Published - 2005|