Theorems · Definition · probability

ProbabilityTheory.Kernel.prodMkLeft

{α : Type u_1} →
  {β : Type u_2} →
    {mα : MeasurableSpace α} →
      {mβ : MeasurableSpace β} →
        (γ : Type u_5) → [inst : MeasurableSpace γ] → ProbabilityTheory.Kernel α β → ProbabilityTheory.Kernel (γ × α) β

Define a Kernel (γ × α) β from a Kernel α β by taking the comap of the projection.

Defined in: Mathlib.Probability.Kernel.Composition.MapComap
Cited by: 38 results in Mathlib
Foundations: Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace

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Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

MeasurableSpacestatement and proof · cited by 13,106
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
measurable_sndproof · cited by 94
ProbabilityTheory.Kernel.comapproof · cited by 34

Cited by39

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.compProdproof · cited by 132
MeasureTheory.Measure.compProd_applyproof · cited by 18
MeasureTheory.Measure.compProd_of_not_isSFiniteKernelproof · cited by 10
MeasureTheory.Measure.compProd_apply_prodproof · cited by 8
MeasureTheory.Measure.compProd_of_not_sfiniteproof · cited by 8
MeasureTheory.Measure.lintegral_compProdproof · cited by 6
MeasureTheory.Measure.compProd_add_leftproof · cited by 4
MeasureTheory.Measure.compProd_congrproof · cited by 4
MeasureTheory.Measure.ae_ae_of_ae_compProdproof · cited by 3
ProbabilityTheory.Kernel.comp_eq_snd_compProdstatement and proof · cited by 2
MeasureTheory.Measure.fst_compProdproof · cited by 2
ProbabilityTheory.HasSubgaussianMGF.add_of_hasCondSubgaussianMGFproof · cited by 2