Theorems · Inductive type · probability
ProbabilityTheory.IsMarkovKernel
{α : Type u_1} →
{β : Type u_2} → {mα : MeasurableSpace α} → {mβ : MeasurableSpace β} → ProbabilityTheory.Kernel α β → PropA kernel is a Markov kernel if every measure in its image is a probability measure.
- Defined in
- Mathlib.Probability.Kernel.Defs
- Cited by
- 124 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 3 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement · cited by 13,106
- ProbabilityTheory.Kernelstatement · cited by 1,281
Cited by135
Results whose statement or proof uses this declaration.
- ProbabilityTheory.bayesRiskproof · cited by 31
- ProbabilityTheory.Kernel.trajstatement and proof · cited by 26
- ProbabilityTheory.Kernel.traj_map_frestrictLestatement and proof · cited by 10
- ProbabilityTheory.Kernel.IndepSets.indepproof · cited by 9
- ProbabilityTheory.Kernel.trajContentstatement and proof · cited by 9
- ProbabilityTheory.Kernel.iIndepFun.indepFun_finsetproof · cited by 8
- ProbabilityTheory.minimaxRiskproof · cited by 6
- ProbabilityTheory.Kernel.exists_ae_eq_isMarkovKernelstatement · cited by 6
- ProbabilityTheory.Kernel.trajFunstatement and proof · cited by 6
- ProbabilityTheory.Kernel.traj_comp_partialTrajstatement and proof · cited by 6
- ProbabilityTheory.Kernel.isProjectiveMeasureFamily_partialTrajstatement and proof · cited by 5
- ProbabilityTheory.eq_zero_or_isMarkovKernelstatement · cited by 5