Proposition 1

— Let T be a locally compact space countable at infinity, $\mu$ a positive measure on T, and $p$ a $\mu$-measurable mapping of T into a locally compact space B. Then there exists a pseudo-image measure of $\mu$ under $p$.

For, there exists a bounded measure $\mu'$ on T equivalent to $\mu$ (Ch. V, §5, No. 6, Prop. 11); $p$ is then $\mu'$-proper.