Theorems · Theorem · functional analysis
lp.norm_zero
∀ {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)], ‖0‖ = 0- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 217 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.
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
- Set.ofPredproof · cited by 6,101
- Norm.normstatement · cited by 5,413
- AddSubgroupstatement · cited by 3,232
- iSupproof · cited by 2,415
- Finset.cardproof · cited by 2,327
- SummationFilter.unconditionalproof · cited by 2,068
- LT.lt.ne'proof · cited by 1,417
- tsumproof · cited by 1,148
Cited by3
Results whose statement or proof uses this declaration.
- lp.norm_eq_zero_iffproof · cited by 0
- lp.norm_negproof · cited by 0
- lp.norm_const_smulproof · cited by 0