Exercise 1, § 3

Assume that the hypotheses of Th. 1 of No. 1 are satisfied. Let h be a locally $\mu$-integrable function such that p is $(h \cdot \mu)$-proper. Show that the function $b \mapsto g(b) = \int h(t) d\lambda_b(t)$, defined locally almost everywhere in B (for the measure $\nu = p(\mu)$) is such that $p(h \cdot \mu) = g \cdot \nu$.