Theorems · Theorem · probability

MeasureTheory.Integrable.integral_comp

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {E : Type u_4} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} [inst : NormedAddCommGroup E] {a : α} {κ : ProbabilityTheory.Kernel α β}
  {η : ProbabilityTheory.Kernel β γ} [inst_1 : NormedSpace ℝ E] ⦃f : γ → E⦄,
  MeasureTheory.Integrable f ((η.comp κ) a) → MeasureTheory.Integrable (fun x => ∫ (y : γ), f y ∂η x) (κ a)

Defined in: Mathlib.Probability.Kernel.Composition.IntegralCompProd
Cited by: 4 results in Mathlib
Foundations: Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace

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Cites19

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

DFunLike.coestatement and proof · cited by 62,936
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpacestatement and proof · cited by 12,499
MeasureTheory.Measurestatement · cited by 10,939
MeasureTheory.integralstatement · cited by 1,779
MeasureTheory.Integrablestatement and proof · cited by 1,367
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
norm_nonnegproof · cited by 725
LE.le.trans_eqproof · cited by 328
MeasureTheory.ae_of_allproof · cited by 137

Cited by4

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.continuous_integral_integral_compproof · cited by 1
ProbabilityTheory.Kernel.integral_integral_sub_compproof · cited by 1
ProbabilityTheory.Kernel.condExp_trajproof · cited by 1
ProbabilityTheory.Kernel.integral_integral_add_compproof · cited by 1