Measure-Preserving Transformation Natural & Formal Sciences Dictionary Definition A measurable map T: X → X on a measure space (X, Σ, μ) that satisfies μ(T^{-1}(A)) = μ(A) for every measurable set A; equivalently, the pushforward measure T_*μ equals μ.
Measure-Preserving Transformation Natural & Formal Sciences Dictionary Definition A measurable map T: X → X on a measure space (X, Σ, μ) that satisfies μ(T^{-1}(A)) = μ(A) for every measurable set A; equivalently, the pushforward measure T_*μ equals μ.