quasiMeasurePreserving_symm — Mathlib

English

For quasi-measure-preserving self-map f, the limsup of the sequence of iterated preimages equals s almost everywhere.

Русский

Для f существует предел верхний для последовательности предобразов итераций множества s равный s почти по μ.

LaTeX

$$limsup (n) (preimage f)^[n] s =_{ae}^{μ} s$$

Lean4

theorem quasiMeasurePreserving_symm (μ : Measure α) (e : α ≃ᵐ β) : Measure.QuasiMeasurePreserving e.symm (μ.map e) μ :=
  ⟨e.symm.measurable, by rw [Measure.map_map, e.symm_comp_self, Measure.map_id] <;> measurability⟩

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