Theorems · Theorem · probability
ProbabilityTheory.Kernel.disintegrate
∀ {α : Type u_1} {β : Type u_2} {Ω : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
{mΩ : MeasurableSpace Ω} (κ : ProbabilityTheory.Kernel α (β × Ω)) (κCond : ProbabilityTheory.Kernel (α × β) Ω)
[κ.IsCondKernel κCond], κ.fst.compProd κCond = κ- Cited by
- 9 results in Mathlib
- Foundations
- Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- ProbabilityTheory.Kernel.compProdstatement · cited by 99
- ProbabilityTheory.Kernel.fststatement · cited by 81
- ProbabilityTheory.Kernel.IsCondKernelstatement and proof · cited by 3
- ProbabilityTheory.Kernel.IsCondKernel.disintegrateproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.condKernel_apply_eq_condKernelproof · cited by 2
- ProbabilityTheory.setIntegral_condKernelproof · cited by 2
- ProbabilityTheory.setLIntegral_condKernelproof · cited by 2
- ProbabilityTheory.setLIntegral_condKernel_eq_measure_prodproof · cited by 0
- MeasureTheory.AEStronglyMeasurable.integral_kernel_condKernelproof · cited by 0
- ProbabilityTheory.integral_condKernelproof · cited by 0
- ProbabilityTheory.lintegral_condKernelproof · cited by 0
- ProbabilityTheory.lintegral_condKernel_memproof · cited by 0
- ProbabilityTheory.Kernel.IsCondKernel.isProbabilityMeasure_aeproof · cited by 0