Multi-Model Cantor Sets

Elizabeth Cockerill

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arXiv · math/0202198

Multi-Model Cantor Sets

Elizabeth Cockerill

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Abstract

In this paper we define a new class of metric spaces, called multi-model Cantor sets. We compute the Hausdorff dimension and show that the Hausdorff measure of a multi-model Cantor set is finite and non-zero. We then show that a bilipschitz map from one multi-model Cantor set to another has constant Radon-Nikodym derivative on some clopen. We use this to obtain an invariant up to bilipschitz homeomorphism.

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Elizabeth Cockerill. 2002-02-19. Multi-Model Cantor Sets. https://arxiv.org/abs/math/0202198

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