Theorems · Theorem · measure theory

MeasureTheory.measure_eq_div_smul

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : Group G] [MeasurableMul₂ G] {s : Set G} [MeasurableInv G]
  (μ' ν' : MeasureTheory.Measure G) [MeasureTheory.SigmaFinite μ'] [MeasureTheory.SigmaFinite ν']
  [μ'.IsMulLeftInvariant] [ν'.IsMulLeftInvariant], ν' s ≠ 0 → ν' s ≠ ⊤ → μ' = (μ' s / ν' s) • ν'

Left invariant Borel measures on a measurable group are unique (up to a scalar).

Defined in

Mathlib.MeasureTheory.Group.Prod

Cited by

2 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceGroupMeasurableMul₂MeasurableInvMeasureTheory.SigmaFiniteMeasureTheory.SigmaFiniteMeasureTheory.Measure.IsMulLeftInvariantMeasureTheory.Measure.IsMulLeftInvariant