Theorems · Theorem · functional analysis
enorm_sum_le_of_le
∀ {ι : Type u_3} {ε : Type u_8} [inst : TopologicalSpace ε] [inst_1 : ESeminormedAddCommMonoid ε] (s : Finset ι)
{f : ι → ε} {n : ι → ENNReal}, (∀ b ∈ s, ‖f b‖ₑ ≤ n b) → ‖∑ b ∈ s, f b‖ₑ ≤ ∑ b ∈ s, n b- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 9,879
- Finset.sumstatement · cited by 5,195
- LE.le.transproof · cited by 3,151
- ENorm.enormstatement and proof · cited by 715
- Finset.sum_le_sumproof · cited by 182
- ESeminormedAddCommMonoidstatement and proof · cited by 21
- enorm_sum_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- HasSum.enorm_le_of_boundedproof · cited by 1