Theorems · Theorem · measure theory

MeasureTheory.quasiMeasurePreserving_add_right

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : AddGroup G] [MeasurableAdd₂ G] (μ : MeasureTheory.Measure G)
  [MeasureTheory.SFinite μ] [MeasurableNeg G] [μ.IsAddLeftInvariant] (g : G),
  MeasureTheory.Measure.QuasiMeasurePreserving (fun h => h + g) μ μ

A left-invariant measure is quasi-preserved by right-addition. This should not be confused with (measurePreserving_add_right μ g).quasiMeasurePreserving.

Defined in

Mathlib.MeasureTheory.Group.Prod

Cited by

3 results in Mathlib

Foundations

Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddGroupMeasurableAdd₂MeasureTheory.SFiniteMeasurableNegMeasureTheory.Measure.IsAddLeftInvariant