Theorems · Theorem · complex analysis
meromorphicNFAt_finprod
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {ι : Type u_3} {f : ι → 𝕜 → 𝕜},
(∀ (i : ι), MeromorphicNFAt (f i) x) → {σ | f σ x = 0}.Subsingleton → MeromorphicNFAt (∏ᶠ (i : ι), f i) xA finprod of meromorphic functions in normal form is in normal form if at most one of the factors vanishes.
- Defined in
- Mathlib.Analysis.Meromorphic.NormalForm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontriviallyNormedField
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.ofPredstatement and proof · cited by 6,101
- Set.Finite.toFinsetproof · cited by 351
- Set.Subsingletonstatement and proof · cited by 276
- finprodstatement · cited by 257
- Function.HasFiniteMulSupportproof · cited by 99
- analyticAt_constproof · cited by 70
- MeromorphicNFAtstatement and proof · cited by 34
- AnalyticAt.meromorphicNFAtproof · cited by 16
- finprod_eq_prodproof · cited by 10
- finprod_of_not_hasFiniteMulSupportproof · cited by 5
- meromorphicNFAt_prodproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- meromorphicNFOn_finprodproof · cited by 0