Exercise 11, § 7

Let X, Y be two locally compact spaces, $\pi : X \to Y$ a continuous mapping, and M a subset of Y such that $\pi^{-1}(M)$ is contained in a countable union of compact sets. Then, for every positive measure $\nu$ on Y that is concentrated on M, there exists a positive measure $\mu$ on X such that $\pi(\mu) = \nu$ (use Exer. 10).