Theorems · Theorem · real analysis
ENNReal.liminf_const_mul_of_ne_top
∀ {α : Type u_1} {f : Filter α} [f.NeBot] {u : α → ENNReal} {a : ENNReal},
a ≠ ⊤ → Filter.liminf (fun x => a * u x) f = a * Filter.liminf u f- Defined in
- Mathlib.Order.Filter.ENNReal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- Bot.botproof · cited by 4,720
- MulZeroClass.zero_mulproof · cited by 1,625
- Filter.NeBotstatement and proof · cited by 853
- Filter.liminfstatement and proof · cited by 198
- Filter.liminf_constproof · cited by 8
- ENNReal.liminf_const_mul_of_ne_zero_of_ne_topproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ENNReal.liminf_mul_const_of_ne_topproof · cited by 0