measurePreserving_mul_right — Mathlib

English

If μ is invariant under right multiplication, then the map x ↦ f(x) g is measure-preserving when f is measure-preserving.

Русский

Если μ инвариантна справа, то отображение x ↦ f(x) g сохраняет меру при условии, что f меропр preserv.

LaTeX

$$$\\text{MeasurePreserving}(f) \\Rightarrow \\text{MeasurePreserving}(x \\mapsto f(x) g)$$$

Lean4

@[to_additive]
theorem measurePreserving_mul_right (μ : Measure G) [IsMulRightInvariant μ] (g : G) : MeasurePreserving (· * g) μ μ :=
  ⟨measurable_mul_const g, map_mul_right_eq_self μ g⟩

Похожие утверждения