Theorems · Definition · general topology
Filter.Eventually
{α : Type u_1} → (α → Prop) → Filter α → Propf.Eventually p or ∀ᶠ x in f, p x mean that {x | p x} ∈ f. E.g., ∀ᶠ x in atTop, p x
means that p holds true for sufficiently large x.
- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 3,134 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 11 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Set.ofPredproof · cited by 6,101
Cited by3,223
Results whose statement or proof uses this declaration.
- Filter.EventuallyEqproof · cited by 1,912
- Filter.Eventually.monostatement and proof · cited by 646
- Filter.Eventually.of_forallstatement · cited by 526
- Filter.Frequentlyproof · cited by 414
- Filter.EventuallyLEproof · cited by 383
- Filter.Tendsto.eventuallystatement and proof · cited by 174
- Filter.Eventually.existsstatement and proof · cited by 168
- Filter.Eventually.andstatement · cited by 157
- MeasureTheory.ae_of_allstatement · cited by 137
- TendstoUniformlyOnproof · cited by 129
- RestrictedProductproof · cited by 117
- Filter.eventually_atTopstatement · cited by 112
Showing the 200 most cited of 3,223.