The authors extend Falconer's dimension theorem to linear projections of self-affine sets, prove the exceptional projections form algebraic varieties, and construct new examples of non-exact-dimensional projected measures and small sumsets.
Dimensions of orthogonal projections of typical self-affine sets and measures
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Projections of self-affine fractals
The authors extend Falconer's dimension theorem to linear projections of self-affine sets, prove the exceptional projections form algebraic varieties, and construct new examples of non-exact-dimensional projected measures and small sumsets.