Theorems · Theorem · complex analysis
Complex.analyticAt_iff_eventually_differentiableAt
∀ {E : Type u} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] [CompleteSpace E] {f : ℂ → E} {c : ℂ},
AnalyticAt ℂ f c ↔ ∀ᶠ (z : ℂ) in nhds c, DifferentiableAt ℂ f zf : ℂ → E is analytic at z iff it's differentiable near z
- Defined in
- Mathlib.Analysis.Complex.CauchyIntegral
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 287 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- nhdsstatement and proof · cited by 5,554
- Filter.Eventuallystatement and proof · cited by 3,134
- CompleteSpacestatement and proof · cited by 2,532
- IsOpenproof · cited by 2,400
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- DifferentiableAtstatement and proof · cited by 617
- AnalyticAtstatement and proof · cited by 321
Cited by1
Results whose statement or proof uses this declaration.
- analyticAt_clogproof · cited by 6