Theorems · Theorem · functional analysis
lp.norm_apply_le_norm
∀ {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)],
p ≠ 0 → ∀ (f : ↥(lp E p)) (i : α), ‖↑f i‖ ≤ ‖f‖- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 219 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- Norm.normstatement and proof · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- eq_or_neproof · cited by 1,117
- ENNReal.toRealproof · cited by 859
- norm_nonnegproof · cited by 725
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
- Real.rpow_nonnegproof · cited by 111
Cited by6
Results whose statement or proof uses this declaration.
- LipschitzOnWith.coordinateproof · cited by 2
- lp.norm_apply_le_of_tendstoproof · cited by 2
- KuratowskiEmbedding.embeddingOfSubset_isometryproof · cited by 1
- lp.lipschitzWith_one_evalproof · cited by 1
- LipschitzOnWith.extend_lp_inftyproof · cited by 0
- lp.norm_monoproof · cited by 0