Theorems · Theorem · measure theory

MeasureTheory.IsFundamentalDomain.setLIntegral_eq

∀ {G : Type u_1} {α : Type u_3} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : MeasurableSpace α] {s t : Set α}
  {μ : MeasureTheory.Measure α} [MeasurableConstSMul G α] [MeasureTheory.SMulInvariantMeasure G α μ] [Countable G],
  MeasureTheory.IsFundamentalDomain G s μ →
    MeasureTheory.IsFundamentalDomain G t μ →
      ∀ (f : α → ENNReal), (∀ (g : G) (x : α), f (g • 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

GroupMulActionMeasurableSpaceMeasurableConstSMulMeasureTheory.SMulInvariantMeasureCountable