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Exact dimensionality and projections of random self-similar measures and sets (2014)

Falconer, K. J., Jin, X.

Oxford University Press

In: Journal of the London Mathematical Society

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Publication Date: 2014-09-18

Description: We study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact dimensional, generalizing a result of Feng and Hu for self-similar measures. This, together with a compact group extension argument, enables us to generalize Hochman and Shmerkin's theorems on projections of deterministic self-similar measures to these random measures without requiring any separation conditions on the underlying sets. We give applications to self-similar sets and fractal percolation, including new results on projections, $C^1$ -images and distance sets.

Print ISSN: 0024-6107

Electronic ISSN: 1469-7750

Topics: Mathematics

Published by Oxford University Press

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