# Fractal dimensions for inclusion hyperspaces and non-additive measures

Author
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
Abstract
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.
Keywords
Hausdorff dimension; box dimension; measure; capacity; self-similarity; iterated function system
DOI
doi:10.15330/ms.50.1.3-21
Reference
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Pages
3-21
Volume
50
Issue
1
Year
2018
Journal
Matematychni Studii
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