Let $(E^k,\mathcal{E}^k,\mu^k)$ be a product measure space. By a rectangle set in $E^k$, we mean a set of the form $A_1\times\ldots\times A_k$ where each $A_i\in \mathcal{E}$.
My question is, for any $A\in \mathcal{E}^k$ such that $\mu^k(A)<\infty$, can one always find $U$ which is a finite union of rectangle sets, such that $\mu^k(A\Delta U)<\epsilon$ for any $\epsilon>0$? Any reference or short proof?