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Lacunarity of self-similar and stochastically self-similar sets. (English) Zbl 0946.28006
In this paper, the author studies the Minkowski measurability and Minkowski content of self-similar and stochastically self-similar sets. The arguments are based on the key renewal theorem (for the deterministic case) and an analogue of the renewal theorem for branching random walks. The main results are applicable to zero sets of stable bridges and to level sets of stable processes.

MSC:
28A80 Fractals
60D05 Geometric probability and stochastic geometry
60K05 Renewal theory
60G52 Stable stochastic processes
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