Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.addProjection_respects_measure_apply

∀ {G : Type u_1} {α : Type u_3} [inst : AddGroup G] [inst_1 : AddAction G α] [inst_2 : MeasurableSpace α]
  {ν : MeasureTheory.Measure α} (μ : MeasureTheory.Measure (Quotient (AddAction.orbitRel G α)))
  [i : MeasureTheory.AddQuotientMeasureEqMeasurePreimage ν μ] {t : Set α},
  MeasureTheory.IsAddFundamentalDomain G t ν →
    ∀ {U : Set (Quotient (AddAction.orbitRel G α))},
      MeasurableSet U → μ U = ν (Quotient.mk (AddAction.orbitRel G α) ⁻¹' U ∩ t)

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

5 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionMeasurableSpaceMeasureTheory.AddQuotientMeasureEqMeasurePreimage