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On random fractals with infinite branching: definition, measurability, dimensions

Artemi Berlinkov (2013)

Annales de l'I.H.P. Probabilités et statistiques

We investigate the definition and measurability questions of random fractals with infinite branching, and find, under certain conditions, a formula for the upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.

On selections of multifunctions

Milan Matejdes (1993)

Mathematica Bohemica

The purpose of this paper is to introduce a definition of cliquishness for multifunctions and to study the search for cliquish, quasi-continuous and Baire measurable selections of compact valued multifunctions. A correction as well as a generalization of the results of [5] are given.

On self-similar subgroups in the sense of IFS

Mustafa Saltan (2018)

Communications in Mathematics

In this paper, we first give several properties with respect to subgroups of self-similar groups in the sense of iterated function system (IFS). We then prove that some subgroups of p -adic numbers p are strong self-similar in the sense of IFS.

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