Theorems · Theorem · measure theory

MeasureTheory.measurePreserving_mul_prod_inv_right

∀ {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] [μ.IsMulRightInvariant] [ν.IsMulRightInvariant],
  MeasureTheory.MeasurePreserving (fun z => (z.1 * z.2, z.1⁻¹)) (μ.prod ν) (μ.prod ν)

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

Defined in

Mathlib.MeasureTheory.Group.Prod

Cited by

0 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceGroupMeasurableMul₂MeasureTheory.SFiniteMeasureTheory.SFiniteMeasurableInvMeasureTheory.Measure.IsMulRightInvariantMeasureTheory.Measure.IsMulRightInvariant