# real analysis – Product measure is measurable on the two sets

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 $$h(x, y)=f(x) g(y)$$