How would I go about showing that $h$ is $(mathcal{S} otimes mathcal{T})-$ measurable if the given conditions hold:

$(X, mathcal{S})$ and $(Y, mathcal{T})$ are measurable spaces and if $f: X rightarrow mathbf{R}$ is $mathcal{S}$ -measurable and $g: Y rightarrow mathbf{R}$ is $mathcal{T}$ -measurable and $h: X times Y rightarrow mathbf{R}$ is defined by $h(x, y)=f(x) g(y)$