Theorems · Theorem · order theory
Filter.blimsup_eq_limsup
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] {f : Filter β} {u : β → α} {p : β → Prop},
Filter.blimsup u f p = Filter.limsup u (f ⊓ Filter.principal {x | p x})- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ConditionallyCompleteLattice
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.
- Filterstatement and proof · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- Filter.Eventuallyproof · cited by 3,134
- InfSet.sInfproof · cited by 935
- Filter.principalstatement · cited by 740
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.limsupstatement · cited by 226
- Filter.blimsupstatement · cited by 40
Cited by6
Results whose statement or proof uses this declaration.
- Filter.blimsup_congrproof · cited by 4
- Filter.blimsup_or_eq_supproof · cited by 2
- Filter.HasBasis.blimsup_eq_iInf_iSupproof · cited by 2
- ENNReal.essSup_piecewiseproof · cited by 2
- Filter.blimsup_eq_limsup_subtypeproof · cited by 1
- Filter.bliminf_eq_liminfproof · cited by 0