Theorems · Theorem · measure theory

MeasureTheory.StronglyMeasurable.dependsOn_of_piFinset

∀ {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}
  {s : Finset ι} [inst_1 : TopologicalSpace Z] [TopologicalSpace.PseudoMetrizableSpace Z] [T1Space Z],
  MeasureTheory.StronglyMeasurable f → DependsOn f ↑s

If a function is strongly 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

1 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceTopologicalSpace.PseudoMetrizableSpaceT1Space