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Suppose that $(X,𝒜)$ is a measurable space and $Y$ is a metrizable, Souslin space. Let ${𝒜}^u$ denote the universal completion of $𝒜$. For $x\in X$, let $\underline{f}(x,·)$ be the lower semicontinuous hull of $f(x,·)$. If $f:X\times Y\to \overline{ℝ}$ is $({𝒜}^u\otimes ℬ\left(Y\right),ℬ\left(\overline{ℝ}\right))$-measurable, then $\underline{f}$ is $({𝒜}^u\otimes ℬ\left(Y\right),ℬ\left(\overline{ℝ}\right))$-measurable.