Theorems · Theorem · probability
ProbabilityTheory.Kernel.compProd_eq_iff
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
{κ η : ProbabilityTheory.Kernel α β} [MeasurableSpace.CountableOrCountablyGenerated α β]
[MeasureTheory.IsFiniteMeasure μ] [ProbabilityTheory.IsFiniteKernel κ] [ProbabilityTheory.IsFiniteKernel η],
μ.compProd κ = μ.compProd η ↔ ⇑κ =ᵐ[μ] ⇑ηTwo finite kernels κ and η are μ-a.e. equal iff the composition-products μ ⊗ₘ κ
and μ ⊗ₘ η are equal.
- Defined in
- Mathlib.Probability.Kernel.CompProdEqIff
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 337 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.coestatement · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- ProbabilityTheory.IsFiniteKernelstatement and proof · cited by 178
- MeasureTheory.Measure.compProdstatement · cited by 132
- MeasurableSpace.CountableOrCountablyGeneratedstatement and proof · cited by 97
- MeasureTheory.Measure.compProd_congrproof · cited by 4
- ProbabilityTheory.Kernel.ae_eq_of_compProd_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_map_mapproof · cited by 0