Theorems · Theorem · measure theory

MeasureTheory.IsFundamentalDomain.measure_zero_of_invariant

∀ {G : Type u_1} {α : Type u_3} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : MeasurableSpace α] {s : Set α}
  {μ : MeasureTheory.Measure α} [MeasurableConstSMul G α] [MeasureTheory.SMulInvariantMeasure G α μ] [Countable G],
  MeasureTheory.IsFundamentalDomain G s μ → ∀ (t : Set α), (∀ (g : G), g • t = t) → μ (t ∩ s) = 0 → μ t = 0

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

4 results in Mathlib

Foundations

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

Assumes

GroupMulActionMeasurableSpaceMeasurableConstSMulMeasureTheory.SMulInvariantMeasureCountable