Домашня та шкільна освіта старообрядців у ХVІІІ – на початку ХХ ст.: аспекти історії

Abstract

The random β-transformation K is isomorphic to a full shift. This relation gives an invariant measure for K that yields the Bernoulli convolution by projection. We study the local dimension of the invariant measure for K for special values of β and use the projection to obtain results on the local dimension of the Bernoulli convolution