Theorems · Theorem · functional analysis
PiTensorProduct.norm_def
∀ {ι : Type u_1} [inst : Fintype ι] {𝕜 : Type u_2} {E : ι → Type u_3} [inst_1 : (i : ι) → SeminormedAddCommGroup (E i)]
[inst_2 : NormedField 𝕜] [inst_3 : (i : ι) → NormedSpace 𝕜 (E i)] (x : PiTensorProduct 𝕜 fun i => E i),
‖x‖ = ⨅ p, PiTensorProduct.projectiveSeminormAux ↑p- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 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.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement · cited by 7,166
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- iInfstatement · cited by 1,690
- NormedFieldstatement and proof · cited by 1,084
- PiTensorProductstatement and proof · cited by 181
- FreeAddMonoidstatement · cited by 145
- PiTensorProduct.liftsstatement · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- PiTensorProduct.projectiveSeminorm_tprod_leproof · cited by 2
- PiTensorProduct.norm_eval_le_projectiveSeminormproof · cited by 2