continuousOn — Mathlib

English

Global continuity on ball: HasFPowerSeriesWithinOnBall.continuousOn implies continuity on the ball around x.

Русский

Глобальная непрерывность на шаре: HasFPowerSeriesWithinOnBall.continuousOn влечёт непрерывность вокруг x.

LaTeX

$$$\text{continuousOn}$$$

Lean4

/-- If a function admits a power series expansion on a ball, then it is continuous there. -/
protected theorem continuousOn (hf : HasFPowerSeriesOnBall f p x r) : ContinuousOn f (EMetric.ball x r) :=
  by
  rw [← hasFPowerSeriesWithinOnBall_univ] at hf
  simpa using hf.continuousOn

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