Suppose $f(x, e): \mathbb{R} \times (0, \infty)\to [0,\infty]$ is right continuous in $x$, and monotone increasing in $e$. Is $f$ jointly measurable?



Are these conditions enough to ensure joint measurability?
This is a direct consequence of the more general Lemma 6.4.6 in V.I. Bogachev, Measure Theory, Vol. 2 (2007).


