Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.setLIntegral_eq_tsum

∀ {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] [Countable G],
  MeasureTheory.IsAddFundamentalDomain G s μ →
    ∀ (f : α → ENNReal) (t : Set α), ∫⁻ (x : α) in t, f x ∂μ = ∑' (g : G), ∫⁻ (x : α) in t ∩ (g +ᵥ s), f x ∂μ

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

2 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionMeasurableSpaceMeasurableConstVAddMeasureTheory.VAddInvariantMeasureCountable