tendstoUniformlyOnFilter — Mathlib

English

TendstoUniformlyOn F f p s is equivalent to TendstoUniformly (λ i x∈s, F i x) (f ∘ x) p.

Русский

Rавномерная сходимость на s эквивалентна TendstoUniformly для ограничения F на s и композиции f ∘ x.

LaTeX

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

Lean4

theorem tendstoUniformlyOnFilter (h : TendstoUniformly F f p) : TendstoUniformlyOnFilter F f p ⊤ := by
  rwa [← tendstoUniformly_iff_tendstoUniformlyOnFilter]

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