Theorems · Theorem · measure theory

MeasureTheory.IsAddFundamentalDomain.addQuotientMeasureEqMeasurePreimage_of_zero

∀ {G : Type u_1} {α : Type u_3} [inst : AddGroup G] [inst_1 : AddAction G α] [inst_2 : MeasurableSpace α]
  {ν : MeasureTheory.Measure α} [MeasureTheory.VAddInvariantMeasure G α ν] [Countable G] [MeasurableConstVAdd G α]
  {s : Set α},
  MeasureTheory.IsAddFundamentalDomain G s ν → ν s = 0 → MeasureTheory.AddQuotientMeasureEqMeasurePreimage ν 0

If an additive fundamental domain has volume 0, then AddQuotientMeasureEqMeasurePreimage holds.

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

1 results in Mathlib

Foundations

Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionMeasurableSpaceMeasureTheory.VAddInvariantMeasureCountableMeasurableConstVAdd