Theorems · Theorem · functional analysis
Finset.nnnorm_prod_le
∀ {ι : Type u_4} {α : Type u_5} [inst : NormedCommRing α] [NormOneClass α] (s : Finset ι) (f : ι → α),
‖∏ i ∈ s, f i‖₊ ≤ ∏ i ∈ s, ‖f i‖₊- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedCommRingNormOneClass
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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
- NNRealstatement · cited by 4,310
- Finset.prodstatement and proof · cited by 2,356
- NNNorm.nnnormstatement and proof · cited by 952
- LE.le.trans_eqproof · cited by 328
- NormedCommRingstatement and proof · cited by 218
- NormOneClassstatement and proof · cited by 136
- NNReal.coe_prodproof · cited by 7
- Finset.norm_prod_leproof · cited by 6
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