Theorems · Theorem · functional analysis
Finset.norm_prod_le
∀ {ι : Type u_4} {α : Type u_5} [inst : NormedCommRing α] [NormOneClass α] (s : Finset ι) (f : ι → α),
‖∏ i ∈ s, f i‖ ≤ ∏ i ∈ s, ‖f i‖- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedCommRingNormOneClass
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.
- Realstatement · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- Norm.normstatement and proof · cited by 5,413
- Multisetproof · cited by 2,627
- Finset.prodstatement · cited by 2,356
- NormedCommRingstatement and proof · cited by 218
- Multiset.Nodupproof · cited by 148
- NormOneClassstatement and proof · cited by 136
- Finset.casesOnproof · cited by 17
- List.norm_prod_leproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- multipliable_one_add_of_summableproof · cited by 4
- summable_finsetProd_of_summable_normproof · cited by 2
- tendsto_tprod_one_add_of_dominated_convergenceproof · cited by 1
- NumberField.norm_norm_le_norm_mul_house_powproof · cited by 0
- Finset.nnnorm_prod_leproof · cited by 0
- NumberField.house_prod_leproof · cited by 0