Theorems · Theorem · complex analysis
Complex.norm_cderiv_lt
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {z : ℂ} {M r : ℝ} {f : ℂ → E},
0 < r → (∀ w ∈ Metric.sphere z r, ‖f w‖ < M) → ContinuousOn f (Metric.sphere z r) → ‖Complex.cderiv r f z‖ < M / r- Cited by
- 1 results in Mathlib
- Foundations
- Depth 264 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- 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
- Norm.normstatement and proof · cited by 5,413
- Set.Nonemptyproof · cited by 2,627
- LT.lt.leproof · cited by 2,189
- ContinuousOnstatement and proof · cited by 1,411
- LE.le.trans_ltproof · cited by 795
- Metric.spherestatement and proof · cited by 371
- IsMaxOnproof · cited by 114
Cited by1
Results whose statement or proof uses this declaration.
- Complex.norm_cderiv_sub_ltproof · cited by 1