Pushforward (Image) Measure
Natural & Formal Sciences Dictionary
Definition
Given a measurable map f : (X, Σ_X) → (Y, Σ_Y) and a measure μ on X, the pushforward (image) measure f_*μ on Y is defined by f_*μ(B)=μ(f^{-1}(B)) for measurable B⊂Y; it is the natural way to transport mass under f.