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Mathematics  2008 

Moreira's Theorem on the arithmetic sum of dynamically defined Cantor sets

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Abstract:

We present a complete proof of a theorem of C.G. Moreira. Under mild checkable conditions, the theorem asserts that the Hausdorff dimension of the arithmetic sum of two dynamically defined Cantor subsets of the real line, equals either the sum of the dimensions or 1, whichever is smaller.

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