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Let denote the central Cantor set generated by a sequence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda =(\lambda _{n})\in \left( 0,\frac{1}{2} \right) ^{\mathbb {N}}$$\end{document}. By the known trichotomy, the difference set of is one of three possible sets: a finite union of closed intervals, a Cantor set, or a Cantorval. Our main result describes effective conditions for which guarantee that is a Cantorval. We show that these conditions can be expressed in several equivalent forms. Under additional assumptions, the measure of the Cantorval is established. We give an application of the proved theorems for the achievement sets of …