Theorems · Theorem · probability
ProbabilityTheory.Kernel.fst_compProd
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
{mγ : MeasurableSpace γ} (κ : ProbabilityTheory.Kernel α β) (η : ProbabilityTheory.Kernel (α × β) γ)
[ProbabilityTheory.IsSFiniteKernel κ] [ProbabilityTheory.IsMarkovKernel η], (κ.compProd η).fst = κ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- MeasurableSetproof · cited by 3,075
- one_mulproof · cited by 2,841
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.lintegralproof · cited by 1,152
- Set.indicatorproof · cited by 723
- MeasureTheory.Measure.extproof · cited by 308
- Set.univ_interproof · cited by 258
- ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
- MeasureTheory.Measure.restrict_applyproof · cited by 159
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.fst_compProdproof · cited by 2
- ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProdproof · cited by 1
- ProbabilityTheory.HasCondDistrib.of_compProdproof · cited by 0
- ProbabilityTheory.bayesRisk_compProd_le_bayesRiskproof · cited by 0