Theorems · Theorem · measure theory

MeasureTheory.Measure.regular_of_isMulLeftInvariant

∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [IsTopologicalGroup G] [inst_3 : MeasurableSpace G]
  [BorelSpace G] [SecondCountableTopology G] {μ : MeasureTheory.Measure G} [MeasureTheory.SigmaFinite μ]
  [μ.IsMulLeftInvariant] {K : Set G}, IsCompact K → (interior K).Nonempty → μ K ≠ ⊤ → μ.Regular

To show that an invariant σ-finite measure is regular it is sufficient to show that it is finite on some compact set with non-empty interior.

Defined in

Mathlib.MeasureTheory.Measure.Haar.Basic

Cited by

0 results in Mathlib

Foundations

Depth 235 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupTopologicalSpaceIsTopologicalGroupMeasurableSpaceBorelSpaceSecondCountableTopologyMeasureTheory.SigmaFiniteMeasureTheory.Measure.IsMulLeftInvariant