Theorems · Theorem · measure theory

MeasureTheory.QuotientMeasureEqMeasurePreimage.isFiniteMeasure_quotient

∀ {G : Type u_1} {α : Type u_3} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : MeasurableSpace α]
  {ν : MeasureTheory.Measure α} [MeasureTheory.SMulInvariantMeasure G α ν] [Countable G] [MeasurableConstSMul G α]
  (μ : MeasureTheory.Measure (Quotient (MulAction.orbitRel G α))) [MeasureTheory.QuotientMeasureEqMeasurePreimage ν μ]
  [hasFun : MeasureTheory.HasFundamentalDomain G α ν],
  MeasureTheory.covolume G α ν ≠ ⊤ → MeasureTheory.IsFiniteMeasure μ

A measure μ on α ⧸ G satisfying QuotientMeasureEqMeasurePreimage and having finite covolume is a finite measure.

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

0 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionMeasurableSpaceMeasureTheory.SMulInvariantMeasureCountableMeasurableConstSMulMeasureTheory.QuotientMeasureEqMeasurePreimageMeasureTheory.HasFundamentalDomain