quasiMeasurePreserving_smul — Mathlib

English

Scaling by a nonzero real r yields quasi-measure-preservation of Haar measure after adjusting by |r|^finrank.

Русский

Умножение на не нуль-реальное число r сохраняет гааровскую меру до масштаба |r|^finrank.

LaTeX

$$QuasiMeasurePreserving_smul μ r$$

Lean4

theorem quasiMeasurePreserving_smul {r : ℝ} (hr : r ≠ 0) : QuasiMeasurePreserving (r • ·) μ μ :=
  by
  refine ⟨measurable_const_smul r, ?_⟩
  rw [map_addHaar_smul μ hr]
  exact smul_absolutelyContinuous

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