Theorems · Theorem · order theory
Filter.limsup_eq
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] {f : Filter β} {u : β → α},
Filter.limsup u f = sInf {a | ∀ᶠ (n : β) in f, u n ≤ a}- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.ofPredstatement · cited by 6,101
- Filter.Eventuallystatement · cited by 3,134
- InfSet.sInfstatement · cited by 935
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.limsupstatement · cited by 226
Cited by4
Results whose statement or proof uses this declaration.
- Filter.limsup_congrproof · cited by 20
- Filter.limsup_const_botproof · cited by 6
- Filter.limsup_eq_sInf_sSupproof · cited by 1
- bsupr_limsup_dimHproof · cited by 1