Theorems · Definition · measure theory
IsAddFoelner.mean
{X : Type u_2} →
[inst : MeasurableSpace X] → MeasureTheory.Measure X → {ι : Type u_3} → Ultrafilter ι → (ι → Set X) → Set X → ENNRealThe limit along an ultrafilter of the density of a set with respect to a sequence in X.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Ultrafilterstatement and proof · cited by 193
- Ultrafilter.toFilterproof · cited by 172
- Filter.limUnderproof · cited by 47
Cited by6
Results whose statement or proof uses this declaration.
- IsAddFoelner.tendsto_nhds_meanstatement · cited by 3
- IsAddFoelner.amenableproof · cited by 1
- IsAddFoelner.mean_union_eq_add_of_disjointstatement · cited by 1
- IsAddFoelner.mean_univ_eq_zerostatement · cited by 1
- IsAddFoelner.mean_vadd_eq_meanstatement and proof · cited by 1
- IsAddFoelner.mean_vadd_eq_mean_vaddstatement and proof · cited by 1