Theorems · Theorem · measure theory

MeasureTheory.measurePreserving_prod_neg_add_swap

∀ {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.IsAddLeftInvariant],
  MeasureTheory.MeasurePreserving (fun z => (z.2, -z.2 + z.1)) (μ.prod ν) (ν.prod μ)

The map (x, y) ↦ (y, - y + x) sends μ × ν to ν × μ.

Defined in

Mathlib.MeasureTheory.Group.Prod

Cited by

2 results in Mathlib

Foundations

Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddGroupMeasurableAdd₂MeasureTheory.SFiniteMeasureTheory.SFiniteMeasurableNegMeasureTheory.Measure.IsAddLeftInvariant