Theorems · Theorem · functional analysis
lp.norm_le_of_forall_le
∀ {α : Type u_3} {E : α → Type u_4} [inst : (i : α) → NormedAddCommGroup (E i)] {f : ↥(lp E ⊤)} {C : ℝ},
0 ≤ C → (∀ (i : α), ‖↑f i‖ ≤ C) → ‖f‖ ≤ C- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Norm.normstatement and proof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- IsEmptyproof · cited by 759
- norm_zeroproof · cited by 366
- isEmpty_or_nonemptyproof · cited by 269
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
- lp.eq_zero'proof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- LipschitzOnWith.coordinateproof · cited by 2
- KuratowskiEmbedding.embeddingOfSubset_dist_leproof · cited by 1
- lp.norm_le_of_tendstoproof · cited by 1
- lp.norm_const_smul_leproof · cited by 1
- lp.norm_monoproof · cited by 0