Theorems · Theorem · functional analysis
Pi.nnnorm_def
∀ {ι : Type u_1} {G : ι → Type u_4} [inst : Fintype ι] [inst_1 : (i : ι) → SeminormedAddGroup (G i)]
(f : (i : ι) → G i), ‖f‖₊ = Finset.univ.sup fun b => ‖f b‖₊- Cited by
- 12 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeSeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- NNRealstatement · cited by 4,310
- Finset.univstatement and proof · cited by 3,473
- NNNorm.nnnormstatement and proof · cited by 952
- norm_nonnegproof · cited by 725
- Finset.supstatement and proof · cited by 530
- SeminormedAddGroupstatement and proof · cited by 331
Cited by12
Results whose statement or proof uses this declaration.
- Matrix.linfty_opNNNorm_eq_opNNNormproof · cited by 2
- Matrix.linfty_opNNNorm_replicateColproof · cited by 2
- PiLp.nnnorm_ofLpproof · cited by 2
- Pi.nnnorm_singleproof · cited by 2
- Matrix.nnnorm_map_eqproof · cited by 2
- NumberField.canonicalEmbedding.nnnorm_eqproof · cited by 2
- Matrix.linfty_opNNNorm_diagonalproof · cited by 1
- NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlaceproof · cited by 1
- Matrix.nnnorm_diagonalproof · cited by 1
- Matrix.nnnorm_replicateColproof · cited by 1
- Matrix.nnnorm_replicateRowproof · cited by 1
- Matrix.norm_eq_sup_sup_nnnormproof · cited by 0