Let $X_i$ be a sequence of probability spaces and define $\displaystyle X=\prod_{i=1}^\infty X_i$
Let $A$ be the algebra on $X$ generated by the sets of the form $\displaystyle \prod_{i=1}^{n-1} X_i \times E_n \times \prod_{i=n+1}^{\infty} X_i, E_n \in P(X_n)$
Show that every element in $A$ can be written as $a= \displaystyle \cup_{j=1}^m (\prod_{i=1}^{n_j} E_{j,i} \times \prod_{i=n_j}^{\infty} X_i)$ where $E_{j,i} \in P(X_i)$ and the union is a disjoint union