Theorems · Definition · order theory
Filter.liminf
{α : Type u_1} → {β : Type u_2} → [ConditionallyCompleteLattice α] → (β → α) → Filter β → αThe liminf of a function u along a filter f is the supremum of the a such that
the inequality u x ≥ a eventually holds for f.
- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 198 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 64 definitions · uses no axioms
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Filter.mapproof · cited by 819
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.limsInfproof · cited by 31
Cited by201
Results whose statement or proof uses this declaration.
- LinearGrowth.linearGrowthInfproof · cited by 41
- ExpGrowth.expGrowthInfproof · cited by 38
- essInfproof · cited by 18
- Filter.eventually_lt_of_lt_liminfstatement and proof · cited by 17
- Filter.liminf_congrstatement · cited by 14
- Filter.Tendsto.liminf_eqstatement · cited by 14
- Filter.liminf_le_liminfstatement · cited by 10
- Filter.le_liminf_iffstatement · cited by 9
- Filter.le_liminf_of_lestatement · cited by 9
- Filter.liminf_conststatement · cited by 8
- tendsto_of_le_liminf_of_limsup_lestatement and proof · cited by 7
- Filter.liminf_le_of_lestatement · cited by 7
Showing the 200 most cited of 201.