Theorems · Theorem · general topology
Finset.nnnorm_prod_le_sup_nnnorm
∀ {M : Type u_1} {ι : Type u_2} [inst : SeminormedCommGroup M] [IsUltrametricDist M] (s : Finset ι) (f : ι → M),
‖∏ i ∈ s, f i‖₊ ≤ s.sup fun x => ‖f x‖₊Nonarchimedean norm of a product is less than or equal to the largest norm of a term in the product.
- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 1 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.
Cites16
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 and proof · cited by 4,310
- Finset.prodstatement and proof · cited by 2,356
- OrderBotproof · cited by 1,055
- Finset.Nonemptyproof · cited by 1,001
- NNNorm.nnnormstatement and proof · cited by 952
- SemilatticeSupproof · cited by 785
- Finset.supstatement · cited by 530
- SeminormedCommGroupstatement and proof · cited by 191
- IsUltrametricDiststatement and proof · cited by 177
- Finset.eq_empty_or_nonemptyproof · cited by 104
- bot_eq_zero'proof · cited by 92
Cited by1
Results whose statement or proof uses this declaration.
- IsUltrametricDist.nnnorm_prod_le_of_forall_leproof · cited by 1