partialSum_continuous — Mathlib

English

If the tail of the sequence is eventually bounded by C, then the radius is at least r.

Русский

Если хвост последовательности в конечном счёте ограничен константой C, тогда радиус не меньше r.

LaTeX

$$le_radius_of_eventually_le (p) (C) (h : ∀ᶠ n in atTop, ‖p n‖ * r^n ≤ C) : ↑r ≤ p.radius$$

Lean4

/-- The partial sums of a formal multilinear series are continuous. -/
theorem partialSum_continuous (p : FormalMultilinearSeries 𝕜 E F) (n : ℕ) : Continuous (p.partialSum n) :=
  by
  unfold partialSum
  fun_prop

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