Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.aestronglyMeasurable_on_iff

∀ {G : Type u_1} {α : Type u_3} [inst : AddGroup G] [inst_1 : AddAction G α] [inst_2 : MeasurableSpace α] {s t : Set α}
  {μ : MeasureTheory.Measure α} [MeasurableConstVAdd G α] [MeasureTheory.VAddInvariantMeasure G α μ] [Countable G]
  {β : Type u_6} [inst_6 : TopologicalSpace β] [TopologicalSpace.PseudoMetrizableSpace β],
  MeasureTheory.IsAddFundamentalDomain G s μ →
    MeasureTheory.IsAddFundamentalDomain G t μ →
      ∀ {f : α → β},
        (∀ (g : G) (x : α), f (g +ᵥ x) = f x) →
          (MeasureTheory.AEStronglyMeasurable f (μ.restrict s) ↔ MeasureTheory.AEStronglyMeasurable f (μ.restrict t))

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

1 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionMeasurableSpaceMeasurableConstVAddMeasureTheory.VAddInvariantMeasureCountableTopologicalSpaceTopologicalSpace.PseudoMetrizableSpace