Theorems · Theorem · functional analysis
LipschitzWith.uniformly_bounded
∀ {α : Type u_3} {ι : Type u_5} [inst : PseudoMetricSpace α] (g : α → ι → ℝ) {K : NNReal},
(∀ (i : ι), LipschitzWith K fun x => g x i) → ∀ (a₀ : α), Memℓp (g a₀) ⊤ → ∀ (a : α), Memℓp (g a) ⊤- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Norm.normproof · cited by 5,413
- Set.rangeproof · cited by 4,705
- NNRealstatement and proof · cited by 4,310
- absproof · cited by 1,814
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- NNReal.toRealproof · cited by 1,260
- add_le_addproof · cited by 666
- sub_add_cancelproof · cited by 344
Cited by1
Results whose statement or proof uses this declaration.
- LipschitzOnWith.extend_lp_inftyproof · cited by 0