Theorems · Theorem · measure theory

MeasureTheory.measure_pos_iff_nonempty_of_vaddInvariant

∀ (G : Type u) {α : Type w} {m : MeasurableSpace α} [inst : AddGroup G] [inst_1 : AddAction G α]
  {μ : MeasureTheory.Measure α} [MeasureTheory.VAddInvariantMeasure G α μ] [inst_3 : TopologicalSpace α]
  [ContinuousConstVAdd G α] [AddAction.IsMinimal G α] {U : Set α} [μ.Regular], μ ≠ 0 → IsOpen U → (0 < μ U ↔ U.Nonempty)

Defined in

Mathlib.MeasureTheory.Group.Action

Cited by

1 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddGroupAddActionMeasureTheory.VAddInvariantMeasureTopologicalSpaceContinuousConstVAddAddAction.IsMinimalMeasureTheory.Measure.Regular