A zero-one property of mixing sequences of events
Louis Sucheston · Bulletin of the American Mathematical Society · 1962
A sequence of events {^4 n }r is mixing if for each event M,P{A n M) -P(i4 n )P(M)-»0; if it is also assumed that P(A n )->a, 0££a^l, {A n } is called mixing with density a.A sequence of events {A n } is zero-one if its tail is trivial; semi-zero-one if every subsequence of {A n } admits a zero-one subsequence.THEOREM 1.A sequence of events is mixing if and only if it is semizero-one.