dependsOn_of_piLE — Mathlib

English

If a function is measurable with respect to the σ-algebra generated by the first coordinates, then it depends only on those coordinates up to i.

Русский

Если функция measurability относится к σ-алгебре, порожденной первыми координатами, то она зависит только от этих координат до i.

LaTeX

$$$$ \text{DependsOn } f (Iic\ i). $$$$

Lean4

/-- If a function is measurable with respect to the σ-algebra generated by the
first coordinates, then it only depends on those first coordinates. -/
theorem _root_.Measurable.dependsOn_of_piLE [MeasurableSpace Z] [MeasurableSingletonClass Z]
    (hf : Measurable[piLE i] f) : DependsOn f (Iic i) :=
  dependsOn_iff_factorsThrough.2 hf.factorsThrough

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