Theorems · Theorem · general topology
Filter.isCoboundedUnder_le_of_le
∀ {α : Type u_1} {ι : Type u_4} [inst : Preorder α] (l : Filter ι) [l.NeBot] {f : ι → α} {x : α},
(∀ (i : ι), x ≤ f i) → Filter.IsCoboundedUnder (fun x1 x2 => x1 ≤ x2) l f- Defined in
- Mathlib.Order.Filter.IsBounded
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderFilter.NeBot
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.
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.NeBotstatement and proof · cited by 853
- Filter.Eventually.of_forallproof · cited by 526
- Filter.IsCoboundedUnderstatement · cited by 102
- Filter.isCoboundedUnder_le_of_eventually_leproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.density_le_oneproof · cited by 4
- ProbabilityTheory.Kernel.density_mono_setproof · cited by 3
- MeasureTheory.tendsto_iff_forall_lipschitz_integral_tendstoproof · cited by 1
- MeasureTheory.MemLp.essSup_norm_condExp_le_essSup_normproof · cited by 1