Slutskyi O. Packing fractal dimension and its properties

The thesis is devoted to the investigation of properties of packing fractal dimension and to applications of the results to the number theory and fractal geometry. These investigations are based on the approach, introduced by author. This approach is based on using the notion of uncentered packing dimension. Some sufficient conditions for packing faithfulness of sets families, generated by wide class of number expansions, have been proved. We establish several new probabilistic, fractal and number theoretical phenomena connected with some wide class of number expansions and, partitionally, with the Cantor series. The results provided in PhD thesis are important from the theoretical point of view for the packing dimension calculation and investigation of its properties for sets and measures constrtucted using Q-adic expansions, Cantor series, f-expansions and other expansions of real numbers.