Theorems · Theorem · probability

ProbabilityTheory.Kernel.parallelComp_comp_copy

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
  {mγ : MeasurableSpace γ} (κ : ProbabilityTheory.Kernel α β) (η : ProbabilityTheory.Kernel α γ),
  (κ.parallelComp η).comp (ProbabilityTheory.Kernel.copy α) = κ.prod η

Defined in: Mathlib.Probability.Kernel.Composition.Prod
Cited by: 3 results in Mathlib
Foundations: Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites6

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
ProbabilityTheory.Kernel.compstatement · cited by 129
ProbabilityTheory.Kernel.prodstatement · cited by 65
ProbabilityTheory.Kernel.parallelCompstatement · cited by 49
ProbabilityTheory.Kernel.copystatement · cited by 29

Cited by3

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.parallelComp_comp_prodproof · cited by 3
MeasureTheory.Measure.compProd_eq_parallelComp_comp_copy_compproof · cited by 2
ProbabilityTheory.Kernel.isDeterministic_iff_isZeroOneMeasureproof · cited by 0