Theorems · Theorem · functional analysis
WithLp.prod_norm_eq_of_L1
∀ {α : Type u_2} {β : Type u_3} [inst : SeminormedAddCommGroup α] [inst_1 : SeminormedAddCommGroup β]
(x : WithLp 1 (α × β)), ‖x‖ = ‖x.fst‖ + ‖x.snd‖- Defined in
- Mathlib.Analysis.Normed.Lp.ProdLp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- WithLpstatement and proof · cited by 345
- div_selfproof · cited by 237
- Real.rpow_oneproof · cited by 114
- WithLp.sndstatement and proof · cited by 76
- WithLp.fststatement and proof · cited by 76
- WithLp.prod_norm_eq_addproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- WithLp.prod_dist_eq_of_L1proof · cited by 1
- WithLp.prod_nnnorm_eq_of_L1proof · cited by 0