norm — Mathlib

English

If f is AEStronglyMeasurable with respect to μ and f takes real values, then the map x ↦ (f(x)) ToNNReal is AEStronglyMeasurable with respect to μ.

Русский

Если f имеет значения в ℝ и является AEStronglyMeasurable по μ, то f.toNNReal также AEStronglyMeasurable по μ.

LaTeX

$$$AEStronglyMeasurable(f, \mu) \Rightarrow AEStronglyMeasurable(\lambda x. (f(x)).toNNReal, \mu)$$$

Lean4

@[fun_prop, measurability]
protected theorem norm {β : Type*} [SeminormedAddCommGroup β] {f : α → β} (hf : AEStronglyMeasurable f μ) :
    AEStronglyMeasurable (fun x => ‖f x‖) μ :=
  continuous_norm.comp_aestronglyMeasurable hf

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