Theorems · Theorem · measure theory

MeasureTheory.quasiMeasurePreserving_inv_mul

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Group G] [MeasurableMul₂ G] (μ ν : MeasureTheory.Measure G)
  [MeasureTheory.SFinite ν] [MeasureTheory.SFinite μ] [MeasurableInv G] [ν.IsMulLeftInvariant],
  MeasureTheory.Measure.QuasiMeasurePreserving (fun p => p.1⁻¹ * p.2) (μ.prod ν) ν

The map (x, y) ↦ x⁻¹ * y is quasi-measure-preserving.

Defined in

Mathlib.MeasureTheory.Group.Prod

Cited by

3 results in Mathlib

Foundations

Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceGroupMeasurableMul₂MeasureTheory.SFiniteMeasureTheory.SFiniteMeasurableInvMeasureTheory.Measure.IsMulLeftInvariant