Theorems · Theorem · probability
MeasureTheory.Measure.compProd_add_left
∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (μ ν : MeasureTheory.Measure α)
[MeasureTheory.SFinite μ] [MeasureTheory.SFinite ν] (κ : ProbabilityTheory.Kernel α β),
(μ + ν).compProd κ = μ.compProd κ + ν.compProd κ- Cited by
- 4 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- add_zeroproof · cited by 2,707
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.SFinitestatement and proof · cited by 449
- ProbabilityTheory.IsSFiniteKernelproof · cited by 248
- add_applyproof · cited by 154
- MeasureTheory.Measure.compProdstatement · cited by 132
- ProbabilityTheory.Kernel.compProdproof · cited by 99
- ProbabilityTheory.Kernel.constproof · cited by 93
- ProbabilityTheory.Kernel.prodMkLeftproof · cited by 38
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.absolutelyContinuous_compProd_of_compProdproof · cited by 1
- MeasureTheory.Measure.AbsolutelyContinuous.mutuallySingular_compProd_iffproof · cited by 1
- ProbabilityTheory.rnDeriv_compProd_withDensity_rnDerivproof · cited by 1
- MeasureTheory.Measure.mutuallySingular_compProd_iffproof · cited by 0