OAI/NumberTheory/DukePrimeDegree/Dynamics/FiniteFlowGenericSets.lean
2 declarations, 0 contain sorry, 0 declared as axioms
One generic set for the finite separating observables
The finite family needed to separate the compact set of limiting shears uses one measurable good set and one common time threshold. Only ergodicity of the actual full real-flow component is used.
- theorem
OAI.DukePrimeDegree.exists_finite_uniform_integer_flow_generic_setline 21 - theorem
OAI.DukePrimeDegree.exists_finite_uniform_root_flow_generic_setline 55Source documentation
The common good set applies to an actual ergodic component of a root flow on the arithmetic quotient.
theorem exists_finite_uniform_root_flow_generic_set {n : ℕ} {i j : Fin n} (hij : i ≠ j) {I : Type*} [Fintype I] (ν : Measure (X n)) [IsProbabilityMeasure ν] (herg : let := rootTranslationAction hij …