On self-similar sets with overlaps and inverse theorems for entropy

Proof-critical source

Winning property of counterexamples to Uniform Littlewood's Conjecture

This paper is included only for the following marked statements:

• Theorem 1.1 · VOR pp. 775–779; proof §§2–5Dimension drop for a self-similar measure forces superexponential cylinder concentration.
• Corollary 1.2 · VOR p. 776Dimension drop for a self-similar set forces superexponential cylinder concentration.
• Theorem 1.6 · VOR pp. 779–781Irrational projections of the one-dimensional Sierpiński gasket have full dimension; its proof supplies the needed separation argument.