Theorems · Theorem · Lie groups

MeasureTheory.isOpenPosMeasure_of_mulLeftInvariant_of_compact

∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : TopologicalSpace G] [BorelSpace G] {μ : MeasureTheory.Measure G}
  [inst_3 : Group G] [IsTopologicalGroup G] [μ.IsMulLeftInvariant] (K : Set G),
  IsCompact K → μ K ≠ 0 → μ.IsOpenPosMeasure

If a left-invariant measure gives positive mass to a compact set, then it gives positive mass to any open set.

Defined in

Mathlib.MeasureTheory.Group.Measure

Cited by

1 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceBorelSpaceGroupIsTopologicalGroupMeasureTheory.Measure.IsMulLeftInvariant