Definition 1

Let T and B be two locally compact spaces, $\mu$ a positive measure on T, and p a $\mu$-measurable mapping of T into B. A positive measure $\nu$ on B is said to be a pseudo-image measure of $\mu$ under p if it satisfies the following condition: for a subset N of B to be locally $\nu$-negligible, it is necessary and sufficient that $\overline{p}^{-1}(N)$ be locally $\mu$-negligible.