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Theorems · Theorem · probability

ProbabilityTheory.Kernel.deterministic_parallelComp_deterministic

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {δ : Type u_4} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {mδ : MeasurableSpace δ} {f : α → γ} {g : β → δ} (hf : Measurable f) (hg : Measurable g),
  (ProbabilityTheory.Kernel.deterministic f hf).parallelComp (ProbabilityTheory.Kernel.deterministic g hg) =
    ProbabilityTheory.Kernel.deterministic (Prod.map f g) ⋯
Defined in
Mathlib.Probability.Kernel.Composition.ParallelComp
Cited by
1 results in Mathlib
Foundations
Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
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MeasureTheory.Measure.compProd_map · cited by 4Measure.compProd_mapDFunLike.coe · cited by 62936DFunLike.coeMeasurableSpace · cited by 13106MeasurableSpaceMeasurable · cited by 1499MeasurableProbabilityTheory.Kernel · cited by 1281ProbabilityTheory.KernelMeasureTheory.Measure.dirac · cited by 210Measure.diracProbabilityTheory.Kernel.ext · cited by 116Kernel.extProbabilityTheory.Kernel.deterministic · cited by 57Kernel.deterministicProbabilityTheory.Kernel.parallelComp · cited by 49Kernel.parallelCompMeasurable.prodMap · cited by 19Measurable.prodMapProbabilityTheory.Kernel.parallelComp_apply · cited by 18Kernel.parallelComp_applyMeasureTheory.Measure.dirac_prod_dirac · cited by 4Measure.dirac_prod_diracKernel.deterministic_parallel…CITED BYCITES

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