Corollary 1

— Let $f$ be a function $\geq 0$ defined on $X$, and let $H$ be the set of $t \in T$ such that $f$ is not $\lambda_t$-negligible. a) If $f$ $\nu$-negligible, then $H$ is locally $\mu$-negligible. b) If $f$ is $\nu$-negligible and $\Lambda$ is vaguely continuous, then $H$ is $\mu$-negligible. c) If $f$ is locally $\nu$-negligible and $\lambda_t^\bullet(1) < +\infty$ locally $\mu$-almost everywhere, then $H$ is locally $\mu$-negligible.