Abstract
In this course we will study generalized Cantor sets and measures. We will see that they share many properties in common with self-similar sets and measures, although new geometric ideas are often needed in the proofs to replace the combinatorial structure of self-similar sets/measures. In particular, under a suitable separation condition the multifractal spectrum of generalized Cantor measures (the set of local dimensions) can be shown to be a closed interval, with one specific local dimension being attained at almost every point of the Cantor set.
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