Theorems · Theorem · measure theory

MeasureTheory.lintegral_lintegral

∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {ν : MeasureTheory.Measure β} [MeasureTheory.SFinite ν] ⦃f : α → β → ENNReal⦄,
  AEMeasurable (Function.uncurry f) (μ.prod ν) →
    ∫⁻ (x : α), ∫⁻ (y : β), f x y ∂ν ∂μ = ∫⁻ (z : α × β), f z.1 z.2 ∂μ.prod ν

The reversed version of Tonelli's Theorem. In this version f is in curried form, which makes it easier for the elaborator to figure out f automatically.

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

3 results in Mathlib

Foundations

Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.SFinite