Theorems · Theorem · functional analysis
enorm_sum_le
∀ {ι : Type u_3} {ε : Type u_9} [inst : TopologicalSpace ε] [inst_1 : ESeminormedAddCommMonoid 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
- 2 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.
Cites10
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
- ENorm.enormstatement and proof · cited by 715
- Eq.leproof · cited by 605
- enorm_zeroproof · cited by 44
- ESeminormedAddCommMonoidstatement and proof · cited by 21
- enorm_add_leproof · cited by 11
- Finset.le_sum_of_subadditiveproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- enorm_sum_le_of_leproof · cited by 1