For diagonal self-affine measures with distinct Lyapunov exponents and exponentially separated one-dimensional projections, Hausdorff dimension equals the minimum of d and the Lyapunov dimension.
On self-similar sets with overlaps an d inverse theorems for entropy
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Dimension of diagonal self-affine measures with exponentially separated projections
For diagonal self-affine measures with distinct Lyapunov exponents and exponentially separated one-dimensional projections, Hausdorff dimension equals the minimum of d and the Lyapunov dimension.