Theorems · Definition · general topology
Filter.Frequently
{α : Type u_1} → (α → Prop) → Filter α → Propf.Frequently p or ∃ᶠ x in f, p x mean that {x | ¬p x} ∉ f. E.g., ∃ᶠ x in atTop, p x
means that there exist arbitrarily large x for which p holds true.
- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 414 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 14 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
- Filter.Eventuallyproof · cited by 3,134
Cited by418
Results whose statement or proof uses this declaration.
- Filter.Frequently.monostatement and proof · cited by 64
- LiouvilleWithproof · cited by 52
- Filter.Frequently.and_eventuallystatement and proof · cited by 49
- Filter.Eventually.frequentlystatement · cited by 44
- MeasureTheory.Measure.supportproof · cited by 41
- Filter.Frequently.existsstatement and proof · cited by 32
- asymptoticConeproof · cited by 26
- Filter.Frequently.of_forallstatement · cited by 25
- Filter.HasBasis.frequently_iffstatement · cited by 16
- mem_closure_iff_frequentlystatement · cited by 15
- Filter.frequently_atTopstatement · cited by 14
- Filter.Tendsto.frequentlystatement and proof · cited by 12
Showing the 200 most cited of 418.