tendsto_at — Mathlib

English

Alternative formulation of TendstoUniformlyOn in terms of subtype access.

Русский

Альтернативная формулировка TendstoUniformlyOn через доступ к подптипу.

LaTeX

$$$$TendstoUniformlyOn F f p s\\iff TendstoUniformly (\\lambda i x: F i x) (f \\circ (Subtype.val)) p.$$$$

Lean4

/-- Uniform convergence implies pointwise convergence. -/
theorem tendsto_at (h : TendstoUniformly F f p) (x : α) : Tendsto (fun n => F n x) p <| 𝓝 (f x) :=
  h.tendstoUniformlyOnFilter.tendsto_at le_top

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