Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.setLIntegral_eq

∀ {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],
  MeasureTheory.IsAddFundamentalDomain G s μ →
    MeasureTheory.IsAddFundamentalDomain G t μ →
      ∀ (f : α → ENNReal), (∀ (g : G) (x : α), f (g +ᵥ x) = f x) → ∫⁻ (x : α) in s, f x ∂μ = ∫⁻ (x : α) in t, f x ∂μ

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

3 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionMeasurableSpaceMeasurableConstVAddMeasureTheory.VAddInvariantMeasureCountable