Let $M_X = (X, \mathcal{F}_X)$ and $M_Y = (Y, \mathcal{F}_Y)$ each be a D1108: Measurable space such that

(i) | $f : X \to Y$ is a D1519: Constant map from $X$ to $Y$ |

Then $f$ is a D201: Measurable map from $M_X$ to $M_Y$.