Theorems · Theorem · general topology
Filter.eventually_smallSets
∀ {α : Type u_1} {l : Filter α} {p : Set α → Prop}, (∀ᶠ (s : Set α) in l.smallSets, p s) ↔ ∃ s ∈ l, ∀ t ⊆ s, p t- Defined in
- Mathlib.Order.Filter.SmallSets
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.Eventuallystatement · cited by 3,134
- Filter.smallSetsstatement · cited by 89
- Set.monotone_powersetproof · cited by 5
- Filter.eventually_lift'_iffproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Filter.eventually_smallSets'proof · cited by 11
- Filter.Eventually.exists_measurable_mem_of_smallSetsproof · cited by 4
- MeasureTheory.Measure.FiniteAtFilter.integrableAtFilterproof · cited by 2
- bsupr_limsup_dimHproof · cited by 1
- iSup_limsup_dimHproof · cited by 0