Theorems · Theorem · functional analysis
WithLp.prod_nnnorm_eq_sup
∀ {α : Type u_2} {β : Type u_3} [inst : SeminormedAddCommGroup α] [inst_1 : SeminormedAddCommGroup β]
(f : WithLp ⊤ (α × β)), ‖f‖₊ = max ‖f.fst‖₊ ‖f.snd‖₊- Defined in
- Mathlib.Analysis.Normed.Lp.ProdLp
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNNorm.nnnormstatement and proof · cited by 952
- WithLpstatement and proof · cited by 345
- NNReal.eqproof · cited by 201
- WithLp.fststatement · cited by 76
- WithLp.sndstatement · cited by 76
Cited by3
Results whose statement or proof uses this declaration.
- WithLp.nnnorm_toLp_inlproof · cited by 2
- WithLp.nnnorm_toLp_inrproof · cited by 2
- WithLp.prod_nnnorm_ofLpproof · cited by 2