Dimensions of subsets of Moran fractals related to frequencies of their codings

The Moran fractal considered in this paper is an extension of the self-similar sets satisfying the open set condition. We consider those subsets of the Moran fractal that are the union of an uncountable number of sets each of which consists of the points with their location codes having prescribed mixed group frequencies. It is proved that the Hausdorff and packing dimensions of each of these subsets coincide and are equal to the supremum of the Hausdorff (or packing) dimensions of the sets in the union. An approach is given to calculate their Hausdorff and packing dimensions. The main advantage of our approach is that we treat these subsets in a unified manner. Another advantage of this approach is that the values of the Hausdorff and packing dimensions do not need to be guessed a priori.