Theorems · Definition · order theory
Filter.limsSup
{α : Type u_1} → [ConditionallyCompleteLattice α] → Filter α → αThe limsSup of a filter f is the infimum of the a such that the inequality
x ≤ a eventually holds for f.
- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallyproof · cited by 3,134
- InfSet.sInfproof · cited by 935
- ConditionallyCompleteLatticestatement and proof · cited by 364
Cited by30
Results whose statement or proof uses this declaration.
- Filter.limsupproof · cited by 226
- Filter.limsup_botproof · cited by 8
- Antitone.map_limsSup_of_continuousAtstatement and proof · cited by 6
- Monotone.map_limsSup_of_continuousAtstatement and proof · cited by 5
- Filter.HasBasis.limsSup_eq_iInf_sSupstatement · cited by 5
- ClusterPt.limsSupstatement and proof · cited by 4
- Filter.limsSup_le_limsSupstatement · cited by 4
- Filter.limsSup_le_limsSup_of_lestatement · cited by 4
- Filter.limsSup_le_of_lestatement · cited by 4
- Filter.lt_mem_sets_of_limsSup_ltstatement and proof · cited by 3
- ClusterPt.le_limsSupstatement and proof · cited by 3
- Filter.frequently_lt_of_lt_limsSupstatement and proof · cited by 3