For systems satisfying approximate Z^d or Z_+^d-product property and asymptotic entropy expansiveness, ergodic measures with any given intermediate entropy are generic in certain natural subspaces, confirming Katok's conjecture.
Burguet, Topological and almost Borel universality for systems with the weak specification property
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Ergodic measures of intermediate entropies for $\mathbb{Z}^{d}$-action
For systems satisfying approximate Z^d or Z_+^d-product property and asymptotic entropy expansiveness, ergodic measures with any given intermediate entropy are generic in certain natural subspaces, confirming Katok's conjecture.