Theorems · Theorem · measure theory

MeasureTheory.IsFundamentalDomain.quotientMeasure_eq

∀ {G : Type u_1} {α : Type u_3} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : MeasurableSpace α]
  (μ : MeasureTheory.Measure α) [Countable G] {s t : Set α} [MeasureTheory.SMulInvariantMeasure G α μ]
  [MeasurableConstSMul G α],
  MeasureTheory.IsFundamentalDomain G s μ →
    MeasureTheory.IsFundamentalDomain G t μ →
      MeasureTheory.Measure.map (Quotient.mk (MulAction.orbitRel G α)) (μ.restrict s) =
        MeasureTheory.Measure.map (Quotient.mk (MulAction.orbitRel G α)) (μ.restrict t)

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

1 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionMeasurableSpaceCountableMeasureTheory.SMulInvariantMeasureMeasurableConstSMul