Theorems · Theorem · probability

ProbabilityTheory.measurableSet_kernel_integrable

∀ {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] ⦃f : α → β → E⦄,
  MeasureTheory.StronglyMeasurable (Function.uncurry f) → MeasurableSet {x | MeasureTheory.Integrable (f x) (κ x)}

Defined in: Mathlib.Probability.Kernel.MeasurableIntegral
Cited by: 1 results in Mathlib
Foundations: Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup ProbabilityTheory.IsSFiniteKernel

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Cites17

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
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
Set.ofPredstatement and proof · cited by 6,101
MeasurableSetstatement and proof · cited by 3,075
MeasureTheory.Integrablestatement · cited by 1,367
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasureTheory.StronglyMeasurablestatement and proof · cited by 363
ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
measurable_constproof · cited by 156
MeasureTheory.HasFiniteIntegralproof · cited by 120

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.StronglyMeasurable.integral_kernel_prod_rightproof · cited by 1