Theorems · Theorem · functional analysis
nnnorm_sum_le
∀ {ι : Type u_3} {E : Type u_5} [inst : SeminormedAddCommGroup E] (s : Finset ι) (f : ι → E),
‖∑ a ∈ s, f a‖₊ ≤ ∑ a ∈ s, ‖f a‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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.
- Finsetstatement and proof · cited by 13,712
- Norm.normproof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- NNRealstatement · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNNorm.nnnormstatement and proof · cited by 952
- NNReal.coe_le_coeproof · cited by 73
- norm_sum_leproof · cited by 25
- NNReal.coe_sumproof · cited by 24
Cited by4
Results whose statement or proof uses this declaration.
- Module.Basis.opNNNorm_leproof · cited by 2
- FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsumproof · cited by 2
- FormalMultilinearSeries.le_comp_radius_of_summableproof · cited by 1
- Polynomial.IsRoot.norm_lt_cauchyBoundproof · cited by 0