Theorems · Theorem · measure theory

MeasureTheory.measurePreserving_add_prod_neg_right

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : AddGroup G] [MeasurableAdd₂ G] (μ ν : MeasureTheory.Measure G)
  [MeasureTheory.SFinite ν] [MeasureTheory.SFinite μ] [MeasurableNeg G] [μ.IsAddRightInvariant] [ν.IsAddRightInvariant],
  MeasureTheory.MeasurePreserving (fun z => (z.1 + z.2, -z.1)) (μ.prod ν) (μ.prod ν)

The map (x, y) ↦ (x + y, - x) 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

MeasurableSpaceAddGroupMeasurableAdd₂MeasureTheory.SFiniteMeasureTheory.SFiniteMeasurableNegMeasureTheory.Measure.IsAddRightInvariantMeasureTheory.Measure.IsAddRightInvariant