Theorems · Theorem · general topology
ENNReal.exists_frequently_lt_of_liminf_ne_top
∀ {ι : Type u_4} {l : Filter ι} {x : ι → ℝ},
Filter.liminf (fun n => ↑(Real.nnabs (x n))) l ≠ ⊤ → ∃ R, ∃ᶠ (n : ι) in l, x n < R- Cited by
- 1 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- Filter.Eventuallyproof · cited by 3,134
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- NNReal.toRealproof · cited by 1,260
Cited by1
Results whose statement or proof uses this declaration.
- ENNReal.exists_upcrossings_of_not_bounded_underproof · cited by 1