What I mean, is, given a product measure space $(X \times Y, \mathcal{S} \otimes \mathcal{T})$, is any $E \in \mathcal{S} \otimes \mathcal{T}$ the limit of a sequence of sets ${E_n}$ composed of finite unions and intersections of rectangles? That is,
Can we find a sequence of sets ${E_i}$ s.t.
$$E = \bigcup_{i=1}^\infty E_i$$
where $E_i$ are each a finite (or perhaps countable?) union of rectangles and complements of rectangles?