Theorems · Theorem · real analysis
ENNReal.limsup_eq_zero_iff
∀ {α : Type u_1} {f : Filter α} [CountableInterFilter f] {u : α → ENNReal}, Filter.limsup u f = 0 ↔ u =ᶠ[f] 0- Defined in
- Mathlib.Order.Filter.ENNReal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CountableInterFilter
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.
- ENNRealstatement and proof · cited by 9,879
- Filterstatement and proof · cited by 8,121
- Filter.EventuallyEqstatement · cited by 1,912
- Filter.limsupstatement · cited by 226
- CountableInterFilterstatement and proof · cited by 78
- limsup_eq_botproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ENNReal.essSup_eq_zero_iffproof · cited by 0