On random fractals with infinite branching: definition, measurability, dimensions
Artemi Berlinkov
TL;DR
This paper explores the foundational aspects of random fractals with infinite branching, establishing their measurability and deriving formulas for their Minkowski and packing dimensions under specific conditions.
Contribution
It introduces a formal definition for such fractals, addresses measurability issues, and provides dimension formulas for random self-similar sets.
Findings
Derived formulas for upper and lower Minkowski dimensions.
Established conditions for measurability of random fractals.
Obtained the packing dimension for random self-similar sets.
Abstract
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
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