For tail-reversing infinite-type IETs, the uniquely ergodic lengths form a dense G_delta subset of the simplex under the l1 topology.
Unique ergodicity for infinite area translation surfaces
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Rauzy-Veech Induction for Infinite-Type IETs
For tail-reversing infinite-type IETs, the uniquely ergodic lengths form a dense G_delta subset of the simplex under the l1 topology.