Theorems · Theorem · measure theory

MeasureTheory.Integrable.prod_left_ae

∀ {α : Type u_1} {β : Type u_2} {E : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} [inst_2 : NormedAddCommGroup E] [MeasureTheory.SFinite ν]
  [MeasureTheory.SFinite μ] ⦃f : α × β → E⦄,
  MeasureTheory.Integrable f (μ.prod ν) → ∀ᵐ (y : β) ∂ν, MeasureTheory.Integrable (fun x => f (x, y)) μ

Defined in

Mathlib.MeasureTheory.Integral.Prod

Cited by

1 results in Mathlib

Foundations

Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceNormedAddCommGroupMeasureTheory.SFiniteMeasureTheory.SFinite