Theorems · Theorem · measure theory

MeasureTheory.quasiMeasurePreserving_neg_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] [MeasurableNeg G] [ν.IsAddLeftInvariant],
  MeasureTheory.Measure.QuasiMeasurePreserving (fun p => -p.1 + p.2) (μ.prod ν) ν

The map (x, y) ↦ -x + y is quasi-measure-preserving.

Defined in

Mathlib.MeasureTheory.Group.Prod

Cited by

3 results in Mathlib

Foundations

Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddGroupMeasurableAdd₂MeasureTheory.SFiniteMeasureTheory.SFiniteMeasurableNegMeasureTheory.Measure.IsAddLeftInvariant