Theorems · Theorem · probability

ProbabilityTheory.Kernel.IsFiniteKernel.integrable

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (μ : MeasureTheory.Measure α)
  [MeasureTheory.IsFiniteMeasure μ] (κ : ProbabilityTheory.Kernel α β) [ProbabilityTheory.IsFiniteKernel κ] {s : Set β},
  MeasurableSet s → MeasureTheory.Integrable (fun x => (κ x).real s) μ

Defined in: Mathlib.Probability.Kernel.Integral
Cited by: 1 results in Mathlib
Foundations: Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.IsFiniteMeasure ProbabilityTheory.IsFiniteKernel

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Cites25

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
Setstatement and proof · cited by 53,352
Realstatement and proof · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
MeasurableSetstatement and proof · cited by 3,075
MeasureTheory.Integrablestatement · cited by 1,367
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
ENNReal.toRealproof · cited by 859
MeasureTheory.Measure.realstatement and proof · cited by 530
abs_of_nonnegproof · cited by 279

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.IsMarkovKernel.integrableproof · cited by 0