Theorems · Theorem · probability

MeasureTheory.StronglyMeasurable.integral_kernel_prod_right

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {κ : ProbabilityTheory.Kernel α β}
  {E : Type u_4} [inst : NormedAddCommGroup E] [ProbabilityTheory.IsSFiniteKernel κ] [inst_2 : NormedSpace ℝ E]
  ⦃f : α → β → E⦄,
  MeasureTheory.StronglyMeasurable (Function.uncurry f) →
    MeasureTheory.StronglyMeasurable fun x => ∫ (y : β), f x y ∂κ x

Defined in: Mathlib.Probability.Kernel.MeasurableIntegral
Cited by: 1 results in Mathlib
Foundations: Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup ProbabilityTheory.IsSFiniteKernel NormedSpace

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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 and proof · cited by 10,939
Set.Elemproof · cited by 7,166
Set.ofPredproof · cited by 6,101
nhdsproof · cited by 5,554
Norm.normproof · cited by 5,413
Set.rangeproof · cited by 4,705
Filter.Tendstoproof · cited by 3,814

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MeasureTheory.StronglyMeasurable.integral_kernel_prod_right'proof · cited by 4