Dimensions and measures of quasi self-similar sets

Author:
K. J. Falconer

Journal:
Proc. Amer. Math. Soc. **106** (1989), 543-554

MSC:
Primary 58F12; Secondary 28A75

DOI:
https://doi.org/10.1090/S0002-9939-1989-0969315-8

MathSciNet review:
969315

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that sets with certain quasi self-similar properties have equal Hausdorff and box-packing dimensions and also have positive and finite Hausdorff measure at the dimensional value. A number of applications of these results to particular examples are given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0969315-8

Keywords:
Dimension,
fractal,
self-similar set,
repeller

Article copyright:
© Copyright 1989
American Mathematical Society