Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum_of_ac

∀ {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]
  {ν : MeasureTheory.Measure α},
  MeasureTheory.IsAddFundamentalDomain G s μ →
    ν.AbsolutelyContinuous μ → ∀ (f : α → ENNReal), ∫⁻ (x : α), f x ∂ν = ∑' (g : G), ∫⁻ (x : α) in g +ᵥ s, f x ∂ν

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

3 results in Mathlib

Foundations

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

Assumes

AddGroupAddActionMeasurableSpaceMeasurableConstVAddMeasureTheory.VAddInvariantMeasureCountable