Invariant measures for -free systems revisited

Abstract For B N, the B -free subshift X is the orbit closure of the characteristic function of the set of B -free integers. We show that many results about invariant measures and entropy, previously only known for the hereditary closure of X, have their analogues for X as well. In particular, we settle in the affirmative a conjecture of Keller about a description of such measures G. Keller. Generalized heredity in B -free systems. Stoch. Dyn. 21 (3) (2021), Paper No. 2140008. A central assumption in our work is that ^* (the Toeplitz sequence that generates the unique minimal component of X) is regular. From this, we obtain natural periodic approximations that we frequently use in our proofs to bound the elements in X from above and below.