English
As above, the toNNReal image of a real-valued strongly measurable function is strongly measurable.
Русский
Повтор: toNNReal образ сильно измеримой функции остаётся сильно измеримым.
LaTeX
$$$\mathrm{StronglyMeasurable}(f) \Rightarrow \mathrm{StronglyMeasurable}(f.toNNReal)$$$
Lean4
/-- The `enorm` of a strongly measurable function is measurable.
Unlike `StrongMeasurable.norm` and `StronglyMeasurable.nnnorm`, this lemma proves measurability,
**not** strong measurability. This is an intentional decision: for functions taking values in
ℝ≥0∞, measurability is much more useful than strong measurability. -/
@[fun_prop, measurability]
protected theorem enorm {_ : MeasurableSpace α} {ε : Type*} [TopologicalSpace ε] [ContinuousENorm ε] {f : α → ε}
(hf : StronglyMeasurable f) : Measurable (‖f ·‖ₑ) :=
(continuous_enorm.comp_stronglyMeasurable hf).measurable
