Fractal dimensions for inclusion hyperspaces and nonadditive measures 

Author 
inna.hlushak81@gmail.com^{1}, oleh.nyk@gmail.com^{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., IvanoFrankivsk, Ukraine

Abstract 
Analogues of Hausdorff dimension, upper and lower box dimensions for the inclusion hyperspaces
and nonadditive 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 selfsimilar inclusion hyperspaces and
selfsimilar nonadditive measures are presented.

Keywords 
Hausdorff dimension; box dimension; measure; capacity; selfsimilarity; iterated function system

DOI 
doi:10.15330/ms.50.1.321

Reference 
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Pages 
321

Volume 
50

Issue 
1

Year 
2018

Journal 
Matematychni Studii

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