Theorems · Theorem · functional analysis
enorm_prod_le
∀ {ι : Type u_3} {ε : Type u_8} [inst : TopologicalSpace ε] [inst_1 : ESeminormedCommMonoid ε] (s : Finset ι)
(f : ι → ε), ‖∏ i ∈ s, f i‖ₑ ≤ ∑ i ∈ s, ‖f i‖ₑ- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetstatement and proof · cited by 13,712
- ENNRealstatement · cited by 9,879
- Finset.sumstatement · cited by 5,195
- Finset.prodstatement · cited by 2,356
- ENorm.enormstatement and proof · cited by 715
- Eq.leproof · cited by 605
- enorm_mul_le'proof · cited by 4
- Finset.apply_prod_le_sum_applyproof · cited by 4
- ESeminormedCommMonoidstatement and proof · cited by 4
- enorm_one'proof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- enorm_prod_le_of_leproof · cited by 0