  The $\mu$-limit set of a cellular automaton is a subshift whose forbidden
patterns are exactly those, whose probabilities tend to zero as time tends to
in- finity. In this article, for a given subshift in a large class of
subshifts, we propose the construction of a cellular automaton which realizes
this subshift as $\mu$-limit set where $\mu$ is the uniform Bernoulli measure.
