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Theorems · Definition · probability

ProbabilityTheory.Kernel.prod

{α : Type u_1} →
  {β : Type u_2} →
    {mα : MeasurableSpace α} →
      {mβ : MeasurableSpace β} →
        {γ : Type u_4} →
          {mγ : MeasurableSpace γ} →
            ProbabilityTheory.Kernel α β → ProbabilityTheory.Kernel α γ → ProbabilityTheory.Kernel α (β × γ)

Product of two kernels. This is meaningful only when the kernels are s-finite.

Defined in
Mathlib.Probability.Kernel.Composition.Prod
Cited by
65 results in Mathlib
Foundations
Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

ProbabilityTheory.Kernel.partialTraj · cited by 44Kernel.partialTrajProbabilityTheory.Kernel.prod_apply · cited by 15Kernel.prod_applyMeasureTheory.Measure.compProd_eq_comp_prod · cited by 10Measure.compProd_eq_comp_…ProbabilityTheory.Kernel.partialTraj_succ_self · cited by 6Kernel.partialTraj_succ_s…ProbabilityTheory.Kernel.prod_apply' · cited by 6Kernel.prod_apply'ProbabilityTheory.Kernel.map_prod_map · cited by 4Kernel.map_prod_mapProbabilityTheory.Kernel.prod_apply_prod · cited by 4Kernel.prod_apply_prodMeasureTheory.Measure.compProd_map · cited by 4Measure.compProd_mapProbabilityTheory.Kernel.lintegral_prod · cited by 3Kernel.lintegral_prodProbabilityTheory.Kernel.traj_map_updateFinset · cited by 3Kernel.traj_map_updateFin…ProbabilityTheory.Kernel.parallelComp_comp_copy · cited by 3Kernel.parallelComp_comp_…ProbabilityTheory.Kernel.parallelComp_comp_prod · cited by 3Kernel.parallelComp_comp_…ProbabilityTheory.Kernel.partialTraj_eq_prod · cited by 3Kernel.partialTraj_eq_prodProbabilityTheory.Kernel.partialTraj_succ_of_le · cited by 3Kernel.partialTraj_succ_o…ProbabilityTheory.Kernel.lintegral_deterministic_prod · cited by 2Kernel.lintegral_determin…MeasurableSpace · cited by 13106MeasurableSpaceProbabilityTheory.Kernel · cited by 1281ProbabilityTheory.KernelProbabilityTheory.Kernel.comp · cited by 129Kernel.compProbabilityTheory.Kernel.parallelComp · cited by 49Kernel.parallelCompProbabilityTheory.Kernel.copy · cited by 29Kernel.copyKernel.prodCITED BYCITES

Cites5

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Cited by66

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