continuousOn_of_finite — Mathlib

English

If p_m = 0 for n ≤ m, then p.changeOrigin x l = 0 whenever n ≤ k + l.

Русский

Если p_m = 0 для n ≤ m, тогда p.changeOrigin x l = 0 при n ≤ k + l.

LaTeX

$$(p.changeOriginSeriesTerm k l s hs) = 0$$

Lean4

/-- The sum of a finite power series is continuous. -/
protected theorem continuousOn_of_finite (p : FormalMultilinearSeries 𝕜 E F) {n : ℕ} (hn : ∀ m, n ≤ m → p m = 0) :
    Continuous p.sum := by
  rw [← continuousOn_univ, ← Metric.emetric_ball_top]
  exact (p.hasFiniteFPowerSeriesOnBall_of_finite hn).continuousOn

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