Theorems · Theorem · measure theory

IsFoelner.mean_union_eq_add_of_disjoint

∀ {G : Type u_1} {X : Type u_2} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X} [inst_1 : Group G]
  [inst_2 : MulAction G X] {ι : Type u_3} {u : Ultrafilter ι} {F : ι → Set X},
  IsFoelner G μ (↑u) F →
    ∀ (s t : Set X),
      MeasurableSet t → Disjoint s t → IsFoelner.mean μ u F (s ∪ t) = IsFoelner.mean μ u F s + IsFoelner.mean μ u F t

Defined in

Mathlib.MeasureTheory.Group.FoelnerFilter

Cited by

1 results in Mathlib

Foundations

Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceGroupMulAction