infNndist — Mathlib

English

Let φ: α → α →L[𝕜] E be measurable; for φ(a) a fixed v ∈ F, the map a ↦ infNndist((φ a) v, s) is measurable.

Русский

Пусть φ: α → F →L[𝕜] E измеримо; для фиксированного v ∈ F отображение a ↦ infNndist((φ a) v, s) измеримо.

LaTeX

$$$\\text{Measurable}(\\phi) \\Rightarrow \\forall v,\\ \\text{Measurable}(a \\mapsto \\operatorname{infNndist}((\\phi a) v, s)).$$$

Lean4

@[measurability, fun_prop]
theorem infNndist {f : β → α} (hf : Measurable f) {s : Set α} : Measurable fun x => infNndist (f x) s :=
  measurable_infNndist.comp hf

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