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Average distances on self-similar sets and higher order average distances of self-similar measures

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The purpose of this paper is twofold: (1) we study different notions of the average distance between two points of a self-similar subset of $${\mathbb {R}}$$R, and (2) we investigate… Click to show full abstract

The purpose of this paper is twofold: (1) we study different notions of the average distance between two points of a self-similar subset of $${\mathbb {R}}$$R, and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of $${\mathbb {R}}$$R.

Keywords: self similar; higher order; distances self; similar measures; average distances; order average

Journal Title: Mathematische Zeitschrift
Year Published: 2017

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