Theorems · Theorem · probability
ProbabilityTheory.Kernel.fst_prod
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
{mγ : MeasurableSpace γ} (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsSFiniteKernel κ]
(η : ProbabilityTheory.Kernel α γ) [ProbabilityTheory.IsMarkovKernel η], (κ.prod η).fst = κ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measureproof · cited by 10,939
- ENNRealproof · cited by 9,879
- one_smulproof · cited by 1,374
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.Measure.mapproof · cited by 858
- ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
- MeasureTheory.Measure.bindproof · cited by 173
- MeasureTheory.IsProbabilityMeasure.measure_univproof · cited by 135
- ProbabilityTheory.IsMarkovKernelstatement and proof · cited by 124
- ProbabilityTheory.Kernel.extproof · cited by 116
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.partialTraj_eq_prodproof · cited by 3
- ProbabilityTheory.Kernel.partialTraj_succ_map_frestrictLe₂proof · cited by 1