Abstract
Recently Dekking and Grimmett have used the theories of branching processes in a random environment and of superbranching processes to find the almostsure box-counting dimension of certain orthogonal projections of random Cantor sets. This note gives a rather shorter and more direct calculation, and also shows that the Hausdorff dimension is almost surely equal to the box-counting dimension. We restrict attention to one-dimensional projections of a plane set—there is no difficulty in extending the proof to higher-dimensional cases.
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References
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Falconer, K.J. Projections of random Cantor sets. J Theor Probab 2, 65–70 (1989). https://doi.org/10.1007/BF01048269
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DOI: https://doi.org/10.1007/BF01048269