Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.restrict_restrict

∀ {G : Type u_1} {α : Type u_3} [inst : AddGroup G] [inst_1 : AddAction G α] [inst_2 : MeasurableSpace α] {s : Set α}
  {μ : MeasureTheory.Measure α} [MeasurableConstVAdd G α] [MeasureTheory.VAddInvariantMeasure G α μ],
  MeasureTheory.IsAddFundamentalDomain G s μ →
    ∀ (g : G) (t : Set α), (μ.restrict t).restrict (g +ᵥ s) = μ.restrict ((g +ᵥ s) ∩ t)

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

3 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionMeasurableSpaceMeasurableConstVAddMeasureTheory.VAddInvariantMeasure