Theorems · Theorem · functional analysis
lp.norm_single
∀ {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)] [inst_1 : DecidableEq α],
0 < p → ∀ (i : α) (x : E i), ‖lp.single p i x‖ = ‖x‖- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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 and proof · cited by 9,879
- Top.topproof · cited by 9,680
- Norm.normstatement and proof · cited by 5,413
- NNRealproof · cited by 4,310
- AddSubgroupstatement · cited by 3,232
- le_reflproof · cited by 2,061
- LT.lt.ne'proof · cited by 1,417
- ENNReal.ofNNRealproof · cited by 1,279
- ENNReal.toRealproof · cited by 859
- norm_nonnegproof · cited by 725
Cited by1
Results whose statement or proof uses this declaration.
- lp.isometry_singleproof · cited by 0