Theorems · Theorem · complex analysis

MeromorphicOn.meromorphicOn_comp_add_const_iff_meromorphicOn

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f : 𝕜 → E} {c : 𝕜} {U : Set 𝕜},
  MeromorphicOn (f ∘ fun x => x + c) U ↔ MeromorphicOn f (U + {c})

MeromorphicOn is invariant under translation.

Defined in: Mathlib.Analysis.Meromorphic.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField NormedAddCommGroup NormedSpace

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Cites12

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
Set.addstatement · cited by 338
MeromorphicAtproof · cited by 160
MeromorphicOnstatement and proof · cited by 141
Set.mem_imageproof · cited by 131
add_neg_cancel_rightproof · cited by 65
Set.image_add_rightproof · cited by 37
Set.add_singletonproof · cited by 16
meromorphicAt_comp_add_const_iff_meromorphicAtproof · cited by 4

Cited by2

Results whose statement or proof uses this declaration.

MeromorphicOn.divisor_comp_add_const_eq_divisorproof · cited by 2
MeromorphicOn.meromorphicOn_fun_comp_add_const_iff_meromorphicOnproof · cited by 0