Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.measure_eq

∀ {G : Type u_1} {α : Type u_3} [inst : AddGroup G] [inst_1 : AddAction G α] [inst_2 : MeasurableSpace α] {s t : Set α}
  {μ : MeasureTheory.Measure α} [MeasurableConstVAdd G α] [MeasureTheory.VAddInvariantMeasure G α μ] [Countable G],
  MeasureTheory.IsAddFundamentalDomain G s μ → MeasureTheory.IsAddFundamentalDomain G t μ → μ s = μ t

If s and t are two fundamental domains of the same action, then their measures are equal.

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

AddGroupAddActionMeasurableSpaceMeasurableConstVAddMeasureTheory.VAddInvariantMeasureCountable