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We prove a general version of the classical Perron-Frobenius convergenceproperty for reducible matrices. We then apply this result to reduciblesubstitutions and use it to produce limit frequencies for factors and henceinvariant measures on the associated subshift. The analogous results are wellknown for primitive substitutions and have found many applications, but forreducible substitutions the tools provided here were so far missing from thetheory.

Perron-Frobenius theory and frequency convergence for reducible substitutions