Theorems · Theorem · complex analysis
MeromorphicOn.deriv
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {U : Set 𝕜}, MeromorphicOn f U → ∀ [CompleteSpace E], MeromorphicOn (deriv f) UDerivatives of meromorphic functions are meromorphic.
- Defined in
- Mathlib.Analysis.Meromorphic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- CompleteSpacestatement and proof · cited by 2,532
- derivstatement · cited by 676
- MeromorphicOnstatement and proof · cited by 141
- MeromorphicAt.derivproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- MeromorphicOn.logDerivproof · cited by 0