Fractal properties of singular probability distributions with independent \(Q^{\ast}\)-digits (Q2386011)

By considering the special class of coverings generated by special partitions, called \(Q^*\)-partitions, of the unit interval the authors manage to study the problem of the determination of the Hausdorff dimension of sets via this special class. In particular the paper is focused on the construction of explicit formulae for the determination of the Hausdorff dimension of singular continuous probability measures with independent ``\(Q^*\)-symbols'' which fractal properties are discussed in details as well as for the determination of the Hausdorff dimension of the topological supports of the corresponding measures.