Theorems · Theorem · Lie groups

MeasureTheory.measure_lt_top_of_isCompact_of_isMulLeftInvariant

∀ {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] (U : Set G),
  IsOpen U → U.Nonempty → μ U ≠ ⊤ → ∀ {K : Set G}, IsCompact K → μ K < ⊤

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