Theorems · Theorem · functional analysis
nnnorm_prod_le
∀ {ι : Type u_3} {E : Type u_5} [inst : SeminormedCommGroup E] (s : Finset ι) (f : ι → E),
‖∏ a ∈ s, f a‖₊ ≤ ∑ a ∈ s, ‖f a‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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Cites10
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 · cited by 5,195
- NNRealstatement · cited by 4,310
- Finset.prodstatement and proof · cited by 2,356
- NNNorm.nnnormstatement and proof · cited by 952
- SeminormedCommGroupstatement and proof · cited by 191
- NNReal.coe_le_coeproof · cited by 73
- NNReal.coe_sumproof · cited by 24
- norm_prod_leproof · cited by 2
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