m(A) . 1) ---+ 00. k=O Proof.
17. Let = P, Pi = P for all ,t. Note that we have taken the indexing Ai, where set to be non-negative integers only. Let F = sets of the form Ai = P for all except finitely manyi. Let A be the algebra generated by F and B the O"-algebra generated by A. ~=() = (Wl,W2,W3, .. ). This left shift on n is not one-one. Let P be a probability measure on P and define m on F by m(A) = Ai' This m is countably additive on F, hence o P(Ai) where A = extends to a countably additive measure on B. For A E F, m(O"-lA) = m(A), so that m satisfies m(O"-l A) = m(A) for all A E B.