Theorems · Theorem · measure theory

amenable_of_maxAddFoelner_neBot

∀ {G : Type u_1} {X : Type u_2} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X} [inst_1 : AddGroup G]
  [inst_2 : AddAction G X] [MeasureTheory.VAddInvariantMeasure G X μ] [(maxAddFoelner G μ).NeBot],
  ∃ m,
    m Set.univ = 1 ∧
      (∀ (s t : Set X), MeasurableSet t → Disjoint s t → m (s ∪ t) = m s + m t) ∧
        ∀ (g : G) (s : Set X), m (g +ᵥ s) = m s

Defined in

Mathlib.MeasureTheory.Group.FoelnerFilter

Cited by

0 results in Mathlib

Foundations

Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddGroupAddActionMeasureTheory.VAddInvariantMeasureFilter.NeBot