What can be said about the measurability of $f(x,\cdot):Y\to\mathbb{R}$ if $f:X\times Y\to\mathbb{R}$ is not measurable?

Question

Assume that $(X,\Sigma)$ and $(Y,\text{T})$ are measurable spaces and the function $f:X\times Y\to\mathbb{R}$ is not measurable. Can we say anything about the (non) measurability of the function $f(x,\cdot):Y\to\mathbb{R}$ for fixed $x\in X$?