In this paper we show that if $(X,\mathcal{ A})$ is a measurable space and if $Y$ is a topological model of a Lawvere theory $\mathcal{ T}$ equipped with $\mathcal{ B}$ the Borel $\sigma$-algebra on $Y$, then the set of $\mathcal{ B}$-measurable functions from $X$ to $Y$, $\operatorname{ Meas}(X,Y)$, is a set-theoretic model of $\mathcal{ T}$. As a corollary we give short proofs of the facts that the set of real-valued measurable functions on a measurable space $X$ is a ring and the set of complex-valued measurable functions from $X$ to $\mathbb{ C}$ is a ring.
Categories: math.FA math.CT