measurePreserving — Mathlib

English

Let f be quasi-ergodic and g be a measure-valued function; if g composed with f equals g, then g is constant a.e.

Русский

Пусть f квазир эргодичен, а g — мера-значение функция; если g ◦ f = g, то g константна почти всюду.

LaTeX

$$$[QuasiErgodic(f, \\\\mu)] \\\\Rightarrow \\\\exists c, g = \\\\text{const α c}$$$

Lean4

protected theorem _root_.Measurable.measurePreserving {f : α → β} (h : Measurable f) (μa : Measure α) :
    MeasurePreserving f μa (map f μa) :=
  ⟨h, rfl⟩

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