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For describing the local structure of a random self‐similar measure we use the multi‐fractal decomposition of its support into sets of points of different local dimension. Under the strong open set condition we compute the Hausdorff dimensions of these sets and the generalized dimensions of the random self‐similar measure. Furthermore, the tangential distribution of the random self‐similar measure is investigated.
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Arbeiter et al. (1996) studied this question.
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