Supplement to paper "On some problems of expansions investigated by P. Erdős et al"

Abstract. Based on a seminal theorem of P. Erdős os et al and using the theory of interval-filling sequences, in this paper we present a generalized result, which ensures the existence of continuum many different fraction expansions,for numbers \(x \in (0, L)\), with digit set \( \{ 0,1 \}\).