On mixing sequences of random variables

In a recent paper [1] the first named author proved the following T heorem 1. Let [£2,61, P] be a probability space (i. e. P = P (Д) a prob­ ability measure defined for sets A belonging to the o-algebra 61 of subsets of the set £2). Let C„ be a sequence of sets such that C0 = £2, C„ £ 61 and P (C „) > 0 for n — 1 , 2 ,___ If for к == 0, 1, 2 , . . . the condition1 (1) lim P (C „ |G ) = A ( 0 < A < 1 ) n > CD