Theorems · Theorem · measure theory

MeasureTheory.Measure.prod_apply_symm

∀ {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] [MeasureTheory.SFinite μ] {s : Set (α × β)},
  MeasurableSet s → (μ.prod ν) s = ∫⁻ (y : β), μ ((fun x => (x, y)) ⁻¹' s) ∂ν

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

5 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFinite