stronglyMeasurable_of_hasCompactMulSupport

English

A continuous function with compact multiplication support is strongly measurable.

Русский

Непрерывная функция с компактной поддержкой умножения сильносильно измерима.

LaTeX

$$$\text{Continuous}(f) \Rightarrow \mathrm{StronglyMeasurable}(f)$, when HasCompactMulSupport holds.$$

Lean4

/-- A continuous function with compact support is strongly measurable. -/
@[to_additive]
theorem _root_.Continuous.stronglyMeasurable_of_hasCompactMulSupport [MeasurableSpace α] [TopologicalSpace α]
    [OpensMeasurableSpace α] [MeasurableSpace β] [TopologicalSpace β] [PseudoMetrizableSpace β] [BorelSpace β] [One β]
    {f : α → β} (hf : Continuous f) (h'f : HasCompactMulSupport f) : StronglyMeasurable f :=
  hf.stronglyMeasurable_of_mulSupport_subset_isCompact h'f (subset_mulTSupport f)

Похожие утверждения