Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum_of_ac

∀ {G : Type u_1} {α : Type u_3} {E : Type u_5} [inst : AddGroup G] [inst_1 : AddAction G α] [inst_2 : MeasurableSpace α]
  [inst_3 : NormedAddCommGroup E] {s : Set α} {μ : MeasureTheory.Measure α} [MeasurableConstVAdd G α]
  [MeasureTheory.VAddInvariantMeasure G α μ] [Countable G] {ν : MeasureTheory.Measure α} [inst_7 : NormedSpace ℝ E],
  MeasureTheory.IsAddFundamentalDomain G s μ →
    ν.AbsolutelyContinuous μ →
      ∀ (f : α → E), MeasureTheory.Integrable f ν → ∫ (x : α), f x ∂ν = ∑' (g : G), ∫ (x : α) in g +ᵥ s, f x ∂ν

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

2 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionMeasurableSpaceNormedAddCommGroupMeasurableConstVAddMeasureTheory.VAddInvariantMeasureCountableNormedSpace