Theorems · Theorem · probability
ProbabilityTheory.Kernel.IsMarkovKernel.map
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
{mγ : MeasurableSpace γ} {f : β → γ} (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsMarkovKernel κ],
Measurable f → ProbabilityTheory.IsMarkovKernel (κ.map f)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Measurablestatement and proof · cited by 1,499
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasurableSet.univproof · cited by 178
- MeasureTheory.IsProbabilityMeasure.measure_univproof · cited by 135
- ProbabilityTheory.IsMarkovKernelstatement and proof · cited by 124
- ProbabilityTheory.Kernel.mapstatement · cited by 84
- Set.preimage_univproof · cited by 46
- ProbabilityTheory.Kernel.map_apply'proof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.exists_measurable_map_eq_unitIntervalproof · cited by 1
- ProbabilityTheory.Kernel.partialTraj_succ_map_frestrictLe₂proof · cited by 1