Definition 5

If $\pi$ is a $\mu$-proper mapping of T into a topological space X, the unique measure $\nu$ on X such that $\nu^\bullet(g) = \mu^\bullet(g \circ \pi)$ for all $g \in \mathscr{F}_+(X)$ is called the image measure of $\mu$ under $\pi$, and is denoted $\pi(\mu)$..