Theorems · Theorem · probability
ProbabilityTheory.eq_zero_or_isMarkovKernel
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (κ : ProbabilityTheory.Kernel α β)
[h : ProbabilityTheory.IsZeroOrMarkovKernel κ], κ = 0 ∨ ProbabilityTheory.IsMarkovKernel κ- Defined in
- Mathlib.Probability.Kernel.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- ProbabilityTheory.IsMarkovKernelstatement · cited by 124
- ProbabilityTheory.IsZeroOrMarkovKernelstatement and proof · cited by 32
- ProbabilityTheory.IsZeroOrMarkovKernel.eq_zero_or_isMarkovKernel'proof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.IndepSets.indepproof · cited by 9
- ProbabilityTheory.Kernel.indep_bot_rightproof · cited by 5
- ProbabilityTheory.Kernel.IndepSets.indep_auxproof · cited by 1
- ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProdproof · cited by 1
- ProbabilityTheory.Kernel.bound_le_oneproof · cited by 0