Theorems · Theorem · measure theory

MeasureTheory.IsFundamentalDomain.hasFiniteIntegral_on_iff

∀ {G : Type u_1} {α : Type u_3} {E : Type u_5} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : MeasurableSpace α]
  [inst_3 : NormedAddCommGroup E] {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 → E},
        (∀ (g : G) (x : α), f (g • x) = f x) →
          (MeasureTheory.HasFiniteIntegral f (μ.restrict s) ↔ MeasureTheory.HasFiniteIntegral f (μ.restrict t))

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

1 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionMeasurableSpaceNormedAddCommGroupMeasurableConstSMulMeasureTheory.SMulInvariantMeasureCountable