Theorems · Theorem · measure theory

MeasureTheory.measurePreserving_prod_add

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

The shear mapping (x, y) ↦ (x, x + y) preserves the measure μ × ν.

Defined in

Mathlib.MeasureTheory.Group.Prod

Cited by

3 results in Mathlib

Foundations

Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddGroupMeasurableAdd₂MeasureTheory.SFiniteMeasureTheory.SFiniteMeasureTheory.Measure.IsAddLeftInvariant