A sufficient condition for weak mixing of substitutions and stationary adic transformations

}t~%" the symbols in such a way that the last symbol 0)~ ({a}) has index 0. By the definition of a and b, the sequence of these concatenations is a sequence of words that is increasing on both sides, and its union is a sequence of symbols from Z that is infinite on both sides. We denote it by x(i, j, m, n' ). We consider the weak closure (in the space of all sequences that are infinite on both sides) of trajectory x(i, j, m, n') with respect to a two-sided shift. We denote it by X ~. We shall call the shift X~ -+ X~ a substitution automorphism. Under the condition that G~ is primitive, X~ does not depend on the choice of the generating quadruple. It is known that T is strictly ergodic [5]. Leningrad Scientific-Industrial Union of Medical Laboratory Technology. Translated from Matematicheskie Zametki, Vol. 44, No~ 6, pp. 785-793, December, 1988. Original article submitted April 28, 1986; revision submitted April ii, 1988.