continuousWithinAt_insert — Mathlib

English

Among HasFPowerSeriesWithinOnBall, tendstoUniformlyOn' implies uniform convergence on insert x s ∩ Ball around x.

Русский

Утверждение tendstoUniformlyOn' в HasFPowerSeriesWithinOnBall означает равномерную сходимость на вставке x s ∩ Ball вокруг x.

LaTeX

$$$\text{tendstoUniformlyOn'}(hf,h) : \; \text{TendstoUniformlyOn}(p.partialSum\,n\,(y-x)) f$ на указанной области$$

Lean4

protected theorem continuousWithinAt_insert (hf : HasFPowerSeriesWithinOnBall f p s x r) :
    ContinuousWithinAt f (insert x s) x :=
  by
  apply (hf.continuousOn.continuousWithinAt (x := x) (by simp [hf.r_pos])).mono_of_mem_nhdsWithin
  exact inter_mem_nhdsWithin _ (EMetric.ball_mem_nhds x hf.r_pos)

Похожие утверждения