Theorems · Theorem · functional analysis
PiLp.nnnorm_toLp_one
∀ {p : ENNReal} {ι : Type u_2} [hp : Fact (1 ≤ p)] [inst : Fintype ι] {β : Type u_5}
[inst_1 : SeminormedAddCommGroup β],
p ≠ ⊤ → ∀ [inst_2 : One β], ‖WithLp.toLp p 1‖₊ = ↑(Fintype.card ι) ^ (1 / p).toReal * ‖1‖₊- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- NNRealstatement · cited by 4,310
- Factstatement and proof · cited by 2,726
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Fintype.cardstatement · cited by 1,386
- NNNorm.nnnormstatement · cited by 952
- ENNReal.toRealstatement · cited by 859
- WithLpstatement · cited by 345
- PiLp.nnnorm_toLp_constproof · cited by 4
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