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I am studying the Koch curve but most resources I have seen do not describe the Koch curve formally and are similar to the Wikipedia page on the subject. For example, I have looked at books like Fractal Geometry by Falconer and Measure, Topology, and Fractal Geometry and found it difficult to build formal proofs based on those constructions.

Does anyone know of a book or accessible paper that discusses the Koch curve and its properties formally?

If you could also refer me to a resource that discusses generalized Cantor sets and Cantor functions with proofs of some of the properties I would really appreciate it.

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Rigorous and self-contained treatment of self-similar sets, including both Koch snowflake and Cantor-type sets, can be found in the excellent book Geometry of Sets and Measures on Euclidean spaces by Mattila.

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