The limit set of a Fuchsian group and Dyn'kin's lemma

A geometric description (like Dyn'kin's lemma for the porous sets) of the sets $E\subset\mathbb T$ such that $\log\operatorname{dist}^{-1}(x,E)$ has bounded lower oscillation (BLO) is given. As a corollary, a new proof of the Shirokov–Semenova theorem on the limit set of a finitely generated Fuchsian group of the second kind is obtained.