Theorems · Theorem · probability

MeasureTheory.Measure.lintegral_condKernel_mem

∀ {β : Type u_1} {Ω : Type u_2} {mβ : MeasurableSpace β} [inst : MeasurableSpace Ω] [inst_1 : StandardBorelSpace Ω]
  [inst_2 : Nonempty Ω] {ρ : MeasureTheory.Measure (β × Ω)} [inst_3 : MeasureTheory.IsFiniteMeasure ρ]
  {s : Set (β × Ω)}, MeasurableSet s → ∫⁻ (x : β), (ρ.condKernel x) {y | (x, y) ∈ s} ∂ρ.fst = ρ s

Defined in

Mathlib.Probability.Kernel.Disintegration.Integral

Cited by

0 results in Mathlib

Foundations

Depth 278 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyMeasureTheory.IsFiniteMeasure