Theorems · Theorem · measure theory

MeasureTheory.StronglyMeasurable.integral_prod_right

∀ {α : Type u_1} {β : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  {ν : MeasureTheory.Measure β} [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace ℝ E] [MeasureTheory.SFinite ν]
  ⦃f : α → β → E⦄,
  MeasureTheory.StronglyMeasurable (Function.uncurry f) → MeasureTheory.StronglyMeasurable fun x => ∫ (y : β), f x y ∂ν

The Bochner integral is measurable. This shows that the integrand of (the right-hand-side of) Fubini's theorem is measurable. This version has f in curried form.

Defined in

Mathlib.MeasureTheory.Integral.Prod

Cited by

1 results in Mathlib

Foundations

Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceNormedAddCommGroupNormedSpaceMeasureTheory.SFinite