Construction of $mu$-Limit Sets

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.