Theorems · Theorem · functional analysis
WithLp.prod_edist_eq_of_L2
∀ {α : Type u_2} {β : Type u_3} [inst : SeminormedAddCommGroup α] [inst_1 : SeminormedAddCommGroup β]
(x y : WithLp 2 (α × β)), edist x y = (edist x.fst y.fst ^ 2 + edist x.snd y.snd ^ 2) ^ (1 / 2)- Defined in
- Mathlib.Analysis.Normed.Lp.ProdLp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- ENNRealstatement · cited by 9,879
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- EDist.ediststatement and proof · cited by 735
- one_divproof · cited by 624
- WithLpstatement and proof · cited by 345
- WithLp.fststatement and proof · cited by 76
- WithLp.sndstatement and proof · cited by 76
- ENNReal.toReal_ofNatproof · cited by 23
- WithLp.prod_edist_eq_addproof · cited by 5
- ENNReal.rpow_ofNatproof · cited by 3
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