Switching on of new bans in random sequences

The problem of generating one probability measure on space of the infinite sequences on finite alphabets with $\sigma$-algebra generated by cylindrical sets out of another probability measure on this space is considered. A new probability measure is arranged to reduce the set of admissible trajectories of random sequences definitely. Inadmissibility of trajectories is defined in terms of specifications of the smallest bans. If a specification of the smallest bans is given, then the powers of support of projections of the new measure can be determined. It gives conditions to construct several sets of functions. These functions and projections of the initial measure define a set of measures on finite spaces which define the only probability measure on the space of infinite sequences.