Theorems · Theorem · probability
MeasureTheory.Measure.compProd_eq_comp_prod
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (μ : MeasureTheory.Measure α)
[MeasureTheory.SFinite μ] (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsSFiniteKernel κ],
μ.compProd κ = μ.bind ⇑(ProbabilityTheory.Kernel.id.prod κ)- Cited by
- 10 results in Mathlib
- Foundations
- Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.SFinitestatement and proof · cited by 449
- ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
- MeasureTheory.Measure.bindstatement and proof · cited by 173
- MeasureTheory.Measure.compProdstatement · cited by 132
- ProbabilityTheory.Kernel.compproof · cited by 129
- ProbabilityTheory.Kernel.constproof · cited by 93
- ProbabilityTheory.Kernel.idstatement and proof · cited by 72
- ProbabilityTheory.Kernel.prodstatement and proof · cited by 65
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.compProd_mapproof · cited by 4
- MeasureTheory.Measure.compProd_eq_parallelComp_comp_copy_compproof · cited by 2
- MeasureTheory.Measure.parallelComp_comp_compProdproof · cited by 1
- MeasureTheory.Measure.isProjectiveLimit_infinitePiNatproof · cited by 1
- ProbabilityTheory.posterior_prod_id_compproof · cited by 1
- ProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_comp_trimproof · cited by 1
- MeasureTheory.Measure.compProd_deterministicproof · cited by 1
- ProbabilityTheory.posterior_compproof · cited by 0
- ProbabilityTheory.condIndepFun_iff_condDistrib_prod_ae_eq_prodMkRightproof · cited by 0