We consider homogeneous STIT tessellations Y in the ℓ-dimensional Euclidean space Rℓ and show the triviality of the tail σ-algebra. This is a sharpening of the mixing result by Lachièze-Rey (2001).
Servet Martínez. Werner Nagel. "STIT tessellations have trivial tail σ-algebra." Adv. in Appl. Probab. 46 (3) 643 - 660, September 2014. https://doi.org/10.1239/aap/1409319553