Theorems · Theorem · complex analysis

Complex.continuousOn_norm_circleTransformBoundingFunction

∀ {R r : ℝ},
  r < R →
    ∀ (z : ℂ),
      ContinuousOn ((fun x => ‖x‖) ∘ Complex.circleTransformBoundingFunction R z) (Metric.closedBall z r ×ˢ Set.univ)

Defined in: Mathlib.MeasureTheory.Integral.CircleTransform
Cited by: 1 results in Mathlib
Foundations: Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound

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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
Complexstatement and proof · cited by 5,565
Norm.normstatement · cited by 5,413
Set.univstatement and proof · cited by 3,945
SProd.sprodstatement and proof · cited by 1,750
ContinuousOnstatement and proof · cited by 1,411
Metric.closedBallstatement and proof · cited by 704
inv_powproof · cited by 140
circleMapproof · cited by 117
continuousOn_constproof · cited by 96
Continuous.comp_continuousOnproof · cited by 52

Cited by1

Results whose statement or proof uses this declaration.

Complex.norm_circleTransformBoundingFunction_leproof · cited by 1