Theorems · Theorem · functional analysis
norm_prod_le
∀ {ι : Type u_3} {E : Type u_5} [inst : SeminormedCommGroup E] (s : Finset ι) (f : ι → E),
‖∏ i ∈ s, f i‖ ≤ ∑ i ∈ s, ‖f i‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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
- Finset.sumstatement · cited by 5,195
- Finset.prodstatement · cited by 2,356
- Eq.leproof · cited by 605
- SeminormedCommGroupstatement and proof · cited by 191
- norm_mul_le'proof · cited by 15
- norm_one'proof · cited by 10
- Finset.apply_prod_le_sum_applyproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- norm_prod_le_of_leproof · cited by 2
- nnnorm_prod_leproof · cited by 0