Theorems · Theorem · general topology
ENNReal.tendsto_atTop_zero_iff_lt_of_antitone
∀ {β : Type u_4} [Nonempty β] [inst : SemilatticeSup β] {f : β → ENNReal},
Antitone f → (Filter.Tendsto f Filter.atTop (nhds 0) ↔ ∀ (ε : ENNReal), 0 < ε → ∃ n, f n < ε)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonemptySemilatticeSup
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.
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- nhdsstatement · cited by 5,554
- mul_oneproof · cited by 3,885
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- LE.le.trans_ltproof · cited by 795
- SemilatticeSupstatement and proof · cited by 785
- ne_of_gtproof · cited by 637
- zero_lt_oneproof · cited by 598
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.exists_measure_iInter_ltproof · cited by 1