Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.measurePreserving_add_quotient_mk

∀ {G : Type u_1} {α : Type u_3} [inst : AddGroup G] [inst_1 : AddAction G α] [inst_2 : MeasurableSpace α]
  {ν : MeasureTheory.Measure α} {𝓕 : Set α},
  MeasureTheory.IsAddFundamentalDomain G 𝓕 ν →
    ∀ (μ : MeasureTheory.Measure (Quotient (AddAction.orbitRel G α)))
      [MeasureTheory.AddQuotientMeasureEqMeasurePreimage ν μ],
      MeasureTheory.MeasurePreserving (Quotient.mk (AddAction.orbitRel G α)) (ν.restrict 𝓕) μ

The quotient map to the additive quotient of α by G is measure-preserving between the restriction of volume to an additive fundamental domain in α and a related measure satisfying AddQuotientMeasureEqMeasurePreimage.

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

1 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionMeasurableSpaceMeasureTheory.AddQuotientMeasureEqMeasurePreimage