How do we prove the similarity dimension equals the Hausdorff dimension if the self-similar set satisfies the open set condition? Which article contains this proof?
2026-03-25 12:29:36.1774441776
Similarity dimension and Hausdorff dimension
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The open set condition, and it use to establish Hausdorff dimension, is due to
Moran, P. A. P., Additive functions of intervals and Hausdorff measure, Proc. Camb. Philos. Soc. 42, 15-23 (1946). ZBL0063.04088.
Moran was a student of Besicovitch at Cambridge at the time.
plug
Section 6.5 in
Edgar, Gerald, Measure, topology, and fractal geometry, Undergraduate Texts in Mathematics, 2nd ed. New York, NY: Springer (ISBN 978-0-387-74748-4/hbk). xv, 268 p. (2008). ZBL1152.28008.