toMeasurableSMul — Mathlib

English

For an additive monoid M with measurable structure and measurable addition, the natural-number SMul action on M is measurable; i.e., n • x is measurable in x for fixed n, and related measurability holds for all n.

Русский

Для аддитивного монада M с измеримым структурой и измеримым сложением, действие целых чисел как умножение на N на M измеримо.

LaTeX

$$$\text{MeasurableSMul}_\mathbb{N} M$$$

Lean4

@[to_additive]
instance (priority := 100) toMeasurableSMul [MeasurableSMul₂ M X] : MeasurableSMul M X
    where
  measurable_const_smul _ := measurable_const.smul measurable_id
  measurable_smul_const _ := measurable_id.smul measurable_const

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