Theorems · Theorem · functional analysis
WithLp.prod_nnnorm_ofLp
∀ {α : Type u_2} {β : Type u_3} [inst : SeminormedAddCommGroup α] [inst_1 : SeminormedAddCommGroup β]
(f : WithLp ⊤ (α × β)), ‖f.ofLp‖₊ = ‖f‖₊- Defined in
- Mathlib.Analysis.Normed.Lp.ProdLp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- NNRealstatement and proof · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNNorm.nnnormstatement and proof · cited by 952
- WithLpstatement and proof · cited by 345
- WithLp.ofLpstatement and proof · cited by 323
- WithLp.fstproof · cited by 76
- WithLp.sndproof · cited by 76
- WithLp.prod_nnnorm_eq_supproof · cited by 3
- WithLp.ofLp_fstproof · cited by 3
- WithLp.ofLp_sndproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- WithLp.prod_norm_ofLpproof · cited by 1
- WithLp.prod_nnnorm_toLpproof · cited by 0