Theorems · Theorem · probability
ProbabilityTheory.Kernel.comp_eq_snd_compProd
∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} {mX : MeasurableSpace X} {mY : MeasurableSpace Y}
{mZ : MeasurableSpace Z} (η : ProbabilityTheory.Kernel Y Z) [ProbabilityTheory.IsSFiniteKernel η]
(κ : ProbabilityTheory.Kernel X Y) [ProbabilityTheory.IsSFiniteKernel κ],
η.comp κ = (κ.compProd (ProbabilityTheory.Kernel.prodMkLeft X η)).snd- Cited by
- 2 results in Mathlib
- Foundations
- Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealproof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.lintegralproof · cited by 1,152
- MeasureTheory.Measure.extproof · cited by 308
- ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
- ProbabilityTheory.Kernel.compstatement · cited by 129
- ProbabilityTheory.Kernel.extproof · cited by 116
- ProbabilityTheory.Kernel.compProdstatement and proof · cited by 99
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.compProd_prodMkLeft_eq_compproof · cited by 1
- ProbabilityTheory.Kernel.snd_compProd_prodMkLeftproof · cited by 0