Theorems · Theorem · general topology
Filter.isBoundedUnder_of
∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {f : Filter β} {u : β → α},
(∃ b, ∀ (x : β), r (u x) b) → Filter.IsBoundedUnder r f uA bounded function u is in particular eventually bounded.
- Defined in
- Mathlib.Order.Filter.IsBounded
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Filter.Eventually.of_forallproof · cited by 526
- Filter.IsBoundedUnderstatement and proof · cited by 247
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.density_nonnegproof · cited by 5
- ProbabilityTheory.Kernel.density_mono_setproof · cited by 3
- RingSeminorm.isBoundedUnderproof · cited by 1
- MeasureTheory.tendsto_of_forall_isOpen_le_liminfproof · cited by 1
- Real.isBoundedUnder_ge_exp_compproof · cited by 0