Theorems · Theorem · real analysis
Real.limsSup_of_not_isBounded
∀ {f : Filter ℝ}, ¬Filter.IsBounded (fun x1 x2 => x1 ≤ x2) f → f.limsSup = 0- Defined in
- Mathlib.Order.Filter.ENNReal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallyproof · cited by 3,134
- InfSet.sInfproof · cited by 935
- Filter.Frequentlyproof · cited by 414
- InfSetproof · cited by 145
- Filter.IsBoundedstatement and proof · cited by 45
- Filter.limsSupstatement · cited by 29
- Real.sInf_emptyproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Real.limsup_of_not_isBoundedUnderproof · cited by 1