Theorems · Theorem · probability

ProbabilityTheory.Kernel.comap_apply

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
  {mγ : MeasurableSpace γ} {g : γ → α} (κ : ProbabilityTheory.Kernel α β) (hg : Measurable g) (c : γ),
  (κ.comap g hg) c = κ (g c)

Defined in: Mathlib.Probability.Kernel.Composition.MapComap
Cited by: 8 results in Mathlib
Foundations: Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites6

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

DFunLike.coestatement · cited by 62,936
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement · cited by 10,939
Measurablestatement and proof · cited by 1,499
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
ProbabilityTheory.Kernel.comapstatement · cited by 34

Cited by8

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.apply_eq_measure_condKernel_of_compProd_eqproof · cited by 2
ProbabilityTheory.Kernel.prod_prodMkRight_comp_deterministic_prodproof · cited by 1
ProbabilityTheory.Kernel.id_comapproof · cited by 1
ProbabilityTheory.Kernel.comap_map_commproof · cited by 1
ProbabilityTheory.Kernel.comap_prodproof · cited by 1
ProbabilityTheory.Kernel.prod_prodMkLeft_comp_prod_deterministicproof · cited by 0
ProbabilityTheory.Kernel.comap_sectLproof · cited by 0
ProbabilityTheory.Kernel.comap_sectRproof · cited by 0