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Local Dimensions of Self-similar Measures Satisfying the Finite Neighbour Condition

By Kathryn Hare and Alex Rutar
We study sets of local dimensions for self-similar measures in \(\mathbb{R}\) satisfying the finite neighbour condition, which is formally stronger than the weak separation condition but satisfied in all known examples. Under a mild technical assumption, we establish that the set of attainable local dimensions is a finite union of... Show more
September 4, 2022
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Local Dimensions of Self-similar Measures Satisfying the Finite Neighbour Condition
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