Theorems · Theorem · Lie groups

MeasureTheory.measure_ne_zero_iff_nonempty_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] [μ.Regular],
  μ ≠ 0 → ∀ {s : Set G}, IsOpen s → (μ s ≠ 0 ↔ s.Nonempty)

Defined in

Mathlib.MeasureTheory.Group.Measure

Cited by

1 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceBorelSpaceGroupIsTopologicalGroupMeasureTheory.Measure.IsMulLeftInvariantMeasureTheory.Measure.Regular