Theorems · Theorem · complex analysis
Differentiable.isExactOn_univ
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : ℂ → E} [CompleteSpace E],
Differentiable ℂ f → Complex.IsExactOn f Set.univMorera's theorem for the complex plane A holomorphic function on ℂ has
primitives.
- Defined in
- Mathlib.Analysis.Complex.HasPrimitives
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 290 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- Set.univstatement · cited by 3,945
- CompleteSpacestatement and proof · cited by 2,532
- Differentiablestatement and proof · cited by 298
- isOpen_univproof · cited by 112
- Differentiable.differentiableOnproof · cited by 40
- Differentiable.continuousproof · cited by 28
- Complex.IsExactOnstatement · cited by 6
- Complex.IsConservativeOn.isExactOn_univproof · cited by 1
- Complex.isConservativeOn_and_continuousOn_iff_isDifferentiableOnproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_univ_re_eqproof · cited by 1