Theorems · Theorem · functional analysis
lp.norm_eq_zero_iff
∀ {α : Type u_3} {E : α → Type u_4} {p : ENNReal} [inst : (i : α) → NormedAddCommGroup (E i)] {f : ↥(lp E p)},
‖f‖ = 0 ↔ f = 0- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
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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 and proof · cited by 5,413
- Set.rangeproof · cited by 4,705
- AddSubgroupstatement · cited by 3,232
- SummationFilter.unconditionalproof · cited by 2,068
- le_antisymmproof · cited by 2,068
- LT.lt.ne'proof · cited by 1,417
- ENNReal.toRealproof · cited by 859
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