Theorems · Theorem · general topology
EReal.liminf_mul_le
∀ {α : Type u_3} {f : Filter α} {u v : α → EReal} [f.NeBot],
0 ≤ᶠ[f] u →
0 ≤ᶠ[f] v →
Filter.limsup u f ≠ 0 ∨ Filter.liminf v f ≠ ⊤ →
Filter.limsup u f ≠ ⊤ ∨ Filter.liminf v f ≠ 0 → Filter.liminf (u * v) f ≤ Filter.limsup u f * Filter.liminf v f- Defined in
- Mathlib.Topology.Instances.EReal.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.NeBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- Filter.NeBotstatement and proof · cited by 853
- LE.le.trans_ltproof · cited by 795
- ERealstatement and proof · cited by 793
- Filter.EventuallyLEstatement and proof · cited by 383
- lt_of_le_of_neproof · cited by 230
- Filter.limsupstatement and proof · cited by 226
- Filter.liminfstatement and proof · cited by 198
- Filter.Eventually.andproof · cited by 157
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.