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Theorems · Theorem · probability

MeasureTheory.Measure.compProd_of_not_isSFiniteKernel

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (μ : MeasureTheory.Measure α)
  (κ : ProbabilityTheory.Kernel α β), ¬ProbabilityTheory.IsSFiniteKernel κ → μ.compProd κ = 0
Defined in
Mathlib.Probability.Kernel.Composition.MeasureCompProd
Cited by
10 results in Mathlib
Foundations
Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Measure.AbsolutelyContinuous.compProd_left · cited by 5AbsolutelyContinuous.comp…MeasureTheory.Measure.MutuallySingular.compProd_of_left · cited by 5MutuallySingular.compProd…MeasureTheory.Measure.AbsolutelyContinuous.compProd_right · cited by 4AbsolutelyContinuous.comp…MeasureTheory.Measure.compProd_add_left · cited by 4Measure.compProd_add_leftMeasureTheory.Measure.absolutelyContinuous_of_compProd · cited by 3Measure.absolutelyContinu…MeasureTheory.Measure.compProd_eq_parallelComp_comp_copy_comp · cited by 2Measure.compProd_eq_paral…ProbabilityTheory.Kernel.HasSubgaussianMGF.prodMkLeft_compProd · cited by 1HasSubgaussianMGF.prodMkL…MeasureTheory.Measure.comp_compProd_comm · cited by 1Measure.comp_compProd_commMeasureTheory.Measure.compProd_assoc · cited by 1Measure.compProd_assocMeasureTheory.Measure.IsCondKernel.isSFiniteKernel · cited by 0IsCondKernel.isSFiniteKer…DFunLike.coe · cited by 62936DFunLike.coeMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureProbabilityTheory.Kernel · cited by 1281ProbabilityTheory.Kernelzero_apply · cited by 251zero_applyProbabilityTheory.IsSFiniteKernel · cited by 248ProbabilityTheory.IsSFini…MeasureTheory.Measure.compProd · cited by 132Measure.compProdProbabilityTheory.Kernel.const · cited by 93Kernel.constProbabilityTheory.Kernel.prodMkLeft · cited by 38Kernel.prodMkLeftProbabilityTheory.Kernel.compProd_of_not_isSFiniteKernel_right · cited by 8Kernel.compProd_of_not_is…ProbabilityTheory.Kernel.isSFiniteKernel_prodMkLeft_unit · cited by 1Kernel.isSFiniteKernel_pr…Measure.compProd_of_not_isSFi…CITED BYCITES

Cites11

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Cited by10

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