Similarity Dimension and Hausdorff-Besicovitch Dimension Coincide for Self-Similar Set

Theorem

Let $S$ be a set which has a self-similarity.

Then the similarity dimension and the Hausdorff-Besicovitch dimension of $S$ are the same.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): fractal
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): fractal