Let $(X,\mathcal{F},\mu)$ be a measure space and let $(Y,\mathcal{G})$ be a measurable space and let $T:(X,\mathcal{F})\to(Y,\mathcal{G})$ be a measurable. We define the pushforward measure of $\mu$ under $T$ as $$T_{\#}\mu(A)=\mu(T^{-1}(A))$$$\forall A\in\mathcal{G}$.