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Self-similar sets in complete metric spaces

Author(s): Andreas Schief
Journal: Proc. Amer. Math. Soc. 124 (1996), 481-490.
MSC (1991): Primary 28A80, 28A78
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Abstract: We develop a theory for Hausdorff dimension and measure of self-similar sets in complete metric spaces. This theory differs significantly from the well-known one for Euclidean spaces. The open set condition no longer implies equality of Hausdorff and similarity dimension of self-similar sets and that $K$ has nonzero Hausdorff measure in this dimension. We investigate the relationship between such properties in the general case.

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