Theorems · Theorem · functional analysis
nnnorm_prod_le_of_le
∀ {ι : Type u_3} {E : Type u_5} [inst : SeminormedCommGroup E] (s : Finset ι) {f : ι → E} {n : ι → NNReal},
(∀ b ∈ s, ‖f b‖₊ ≤ n b) → ‖∏ b ∈ s, f b‖₊ ≤ ∑ b ∈ s, n b- 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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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
- Finset.sumstatement · cited by 5,195
- NNRealstatement and proof · cited by 4,310
- Finset.prodstatement · cited by 2,356
- NNNorm.nnnormstatement and proof · cited by 952
- LE.le.trans_eqproof · cited by 328
- SeminormedCommGroupstatement and proof · cited by 191
- NNReal.coe_sumproof · cited by 24
- norm_prod_le_of_leproof · cited by 2
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