Theorems · Theorem · measure theory

IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd

∀ {G : Type u_1} {X : Type u_2} [inst : MeasurableSpace X] {μ : MeasureTheory.Measure X} [inst_1 : AddGroup G]
  [inst_2 : AddAction G X] {ι : Type u_3} {u : Ultrafilter ι} {F : ι → Set X}
  [MeasureTheory.VAddInvariantMeasure G X μ],
  IsAddFoelner G μ (↑u) F →
    ∀ (g h : G), Filter.Tendsto (fun i => μ (symmDiff (g +ᵥ F i) (h +ᵥ F i)) / μ (F i)) (↑u) (nhds 0)

Defined in

Mathlib.MeasureTheory.Group.FoelnerFilter

Cited by

1 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceAddGroupAddActionMeasureTheory.VAddInvariantMeasure