Theorems · Theorem · probability
MeasureTheory.Measure.snd_compProd
∀ {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).snd = μ.bind ⇑κ- Cited by
- 11 results in Mathlib
- Foundations
- Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- Set.preimageproof · cited by 4,946
- MeasurableSetproof · cited by 3,075
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.lintegralproof · cited by 1,152
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasureTheory.Measure.extproof · cited by 308
- ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
Cited by11
Results whose statement or proof uses this declaration.
- ProbabilityTheory.compProd_posterior_eq_map_swapproof · cited by 4
- ProbabilityTheory.condExpKernel_comp_trimproof · cited by 4
- ProbabilityTheory.Kernel.HasSubgaussianMGF.prodMkLeft_compProdproof · cited by 1
- MeasureTheory.Measure.prodMkLeft_comp_compProdproof · cited by 1
- ProbabilityTheory.posterior_comp_selfproof · cited by 1
- ProbabilityTheory.Kernel.setIntegral_traj_partialTrajproof · cited by 1
- ProbabilityTheory.HasCondDistrib.hasLaw_of_constproof · cited by 0
- ProbabilityTheory.condDistrib_comp_mapproof · cited by 0
- MeasureTheory.Measure.integrable_compProd_snd_iffproof · cited by 0
- ProbabilityTheory.Kernel.integral_traj_partialTrajproof · cited by 0
- InformationTheory.klDiv_comp_right_leproof · cited by 0