hasProd — Mathlib

English

If h is MultipliableUniformlyOn f 𝔖, then for any s∈𝔖 and x∈s, Multipliable (f · x).

Русский

Если h = MultipliableUniformlyOn f 𝔖, тогда для любого s∈𝔖 и x∈s верно Multipliable (f · x).

LaTeX

$$$ (h : MultipliableUniformlyOn f 𝔖) \to (hs \in 𝔖) (hx ∈ s) \Rightarrow Multipliable (f \cdot x) $$$

Lean4

@[to_additive]
theorem hasProd (h : HasProdLocallyUniformlyOn f g s) (hx : x ∈ s) : HasProd (f · x) (g x) :=
  h.tendsto_at hx

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