Question: Let Ei , i 2 N, be countable sets and D Q i1 Ei their Cartesian product. Denote by Xi W ! Ei the projection

Let Ei , i 2 N, be countable sets and D Q

i1 Ei their Cartesian product. Denote by Xi W ! Ei the projection onto the i th coordinate. Show that the system G D

®

¹X1 D x1; : : : ; Xk D xkº W k  1; xi 2 Ei

¯

[

®

¿

¯

is an intersection-stable generator of the product -algebra N

i1P.Ei /.

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