Theorems · Theorem · probability
ProbabilityTheory.compProd_trim_condExpKernel
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω] [inst : StandardBorelSpace Ω]
{μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ] (hm : m ≤ mΩ),
(μ.trim hm).compProd (ProbabilityTheory.condExpKernel μ m) = MeasureTheory.Measure.map Function.diag μ- Defined in
- Mathlib.Probability.Kernel.Condexp
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- ProbabilityTheory.Kernelproof · cited by 1,281
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.Measure.mapstatement and proof · cited by 858
- IsEmptyproof · cited by 759
- DFunLikeproof · cited by 576
- MeasureTheory.Measure.extproof · cited by 308
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.condExpKernel_comp_trimproof · cited by 4
- ProbabilityTheory.HasSubgaussianMGF.add_of_hasCondSubgaussianMGFproof · cited by 2
- ProbabilityTheory.condIndepFun_iff_map_prod_eq_prod_comp_trimproof · cited by 1