Fractal dimensions for inclusion hyperspaces and non-additive measures

I. Hlushak2, O. Nykyforchyn1,2
1) Kasimir the Great University in Bydgoszcz Institute of Mathematics, Bydgoszcz, Poland; 2) Vasyl Stefanyk Precarpathian National University Department of Mathematics and Computer Science 57 Shevchenka St., Ivano-Frankivsk, Ukraine
Analogues of Hausdorff dimension, upper and lower box dimensions for the inclusion hyperspaces and non-additive regular measures (capacities) on metric compacta are introduced. Their relations to the respective dimensions of sets and additive measures are investigated. Methods for finding and estimating fractal dimensions of self-similar inclusion hyperspaces and self-similar non-additive measures are presented.
Hausdorff dimension; box dimension; measure; capacity; self-similarity; iterated function system
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