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