Theorems · Theorem · measure theory

Measurable.dependsOn_of_piLE

∀ {Z : Type u_3} {ι : Type u_4} {X : ι → Type u_5} [inst : (i : ι) → MeasurableSpace (X i)] {f : ((i : ι) → X i) → Z}
  [inst_1 : Preorder ι] {i : ι} [inst_2 : MeasurableSpace Z] [MeasurableSingletonClass Z],
  Measurable f → DependsOn f (Set.Iic i)

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

Defined in

Mathlib.MeasureTheory.Function.FactorsThrough

Cited by

0 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpacePreorderMeasurableSpaceMeasurableSingletonClass