Theorems · Theorem · complex analysis
Complex.circleTransformDeriv_bound
∀ {R : ℝ},
0 < R →
∀ {z x : ℂ} {f : ℂ → ℂ},
x ∈ Metric.ball z R →
ContinuousOn f (Metric.sphere z R) →
∃ B ε,
0 < ε ∧
Metric.ball x ε ⊆ Metric.ball z R ∧
∀ (t : ℝ), ∀ y ∈ Metric.ball x ε, ‖Complex.circleTransformDeriv R z y f t‖ ≤ BThe derivative of a circleTransform is locally bounded.
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- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
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