Theorems · Theorem · measure theory

MeasureTheory.quasiMeasurePreserving_mul_right

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Group G] [MeasurableMul₂ G] (μ : MeasureTheory.Measure G)
  [MeasureTheory.SFinite μ] [MeasurableInv G] [μ.IsMulLeftInvariant] (g : G),
  MeasureTheory.Measure.QuasiMeasurePreserving (fun h => h * g) μ μ

A left-invariant measure is quasi-preserved by right-multiplication. This should not be confused with (measurePreserving_mul_right μ g).quasiMeasurePreserving.

Defined in

Mathlib.MeasureTheory.Group.Prod

Cited by

3 results in Mathlib

Foundations

Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceGroupMeasurableMul₂MeasureTheory.SFiniteMeasurableInvMeasureTheory.Measure.IsMulLeftInvariant