Theorems · Theorem · functional analysis
nnnorm_prod
∀ {α : Type u_2} {β : Type u_3} [inst : SeminormedCommRing α] [NormMulClass α] [NormOneClass α] (s : Finset β)
(f : β → α), ‖∏ b ∈ s, f b‖₊ = ∏ b ∈ s, ‖f b‖₊- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 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.
- Finsetstatement and proof · cited by 13,712
- NNRealstatement · cited by 4,310
- Finset.prodstatement · cited by 2,356
- NNNorm.nnnormstatement · cited by 952
- NormOneClassstatement and proof · cited by 136
- map_prodproof · cited by 108
- NormMulClassstatement and proof · cited by 66
- MonoidWithZeroHom.toMonoidHomproof · cited by 39
- SeminormedCommRingstatement and proof · cited by 38
- nnnormHomproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.sub_one_pow_totient_lt_cyclotomic_evalproof · cited by 2
- Polynomial.cyclotomic_eval_lt_add_one_pow_totientproof · cited by 1