Let $(X,\mathcal F)$ and $(Y,\mathcal G)$ be measurable spaces, and let $\mathcal F\otimes\mathcal G$ be the product sigma-algebra on $X\times Y$. The projections
\begin{align*}
\pi_X:X\times Y &\to X,\\
\pi_Y:X\times Y &\to Y
\end{align*}
are measurable.