Theorems · Theorem · complex analysis
DifferentiableOn.isExactOn_ball
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {c : ℂ} {r : ℝ} {f : ℂ → E} [CompleteSpace E],
DifferentiableOn ℂ f (Metric.ball c r) → Complex.IsExactOn f (Metric.ball c r)Morera's theorem for a disk On a disk, a holomorphic function has primitives.
- Defined in
- Mathlib.Analysis.Complex.HasPrimitives
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 272 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- CompleteSpacestatement and proof · cited by 2,532
- Metric.ballstatement and proof · cited by 735
- DifferentiableOnstatement and proof · cited by 419
- DifferentiableOn.continuousOnproof · cited by 32
- Complex.IsExactOnstatement · cited by 6
- Complex.IsConservativeOn.isExactOn_ballproof · cited by 2
- DifferentiableOn.isConservativeOnproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4