Theorems · Theorem · measure theory

MeasureTheory.IsFundamentalDomain.sum_restrict_of_ac

∀ {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]
  {ν : MeasureTheory.Measure α},
  MeasureTheory.IsFundamentalDomain G s μ →
    ν.AbsolutelyContinuous μ → (MeasureTheory.Measure.sum fun g => ν.restrict (g • s)) = ν

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

4 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionMeasurableSpaceMeasurableConstSMulMeasureTheory.SMulInvariantMeasureCountable