measurable_derivWithin_Ioi — Mathlib

English

The measurableSet of differentiableAt with a parameter is measurable under suitable conditions (hf continuous).

Русский

Измеримо множество DifferentiableAt с параметром при соответствующих условиях.

LaTeX

$$MeasurableSet {p : \\alpha × E | DifferentiableAt 𝕜 (f p.1) p.2 ∧ fderiv 𝕜 (f p.1) p.2 ∈ K}$$

Lean4

@[measurability, fun_prop]
theorem measurable_derivWithin_Ioi [MeasurableSpace F] [BorelSpace F] : Measurable fun x => derivWithin f (Ioi x) x :=
  by simpa [derivWithin_Ioi_eq_Ici] using measurable_derivWithin_Ici f

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