Theorems · Theorem · probability

ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {κ : ProbabilityTheory.Kernel α (β × ℝ)} {ν : ProbabilityTheory.Kernel α β} {f : α × β → ℚ → ℝ},
  ProbabilityTheory.IsRatCondKernelCDFAux f κ ν →
    ∀ [ProbabilityTheory.IsFiniteKernel ν] (a : α) (q : ℚ), MeasureTheory.Integrable (fun t => ⨅ r, f (a, t) ↑r) (ν a)

Defined in: Mathlib.Probability.Kernel.Disintegration.CDFToKernel
Cited by: 2 results in Mathlib
Foundations: Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ProbabilityTheory.IsFiniteKernel

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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
Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement · cited by 10,939
Set.Elemstatement and proof · cited by 7,166
Set.rangeproof · cited by 4,705
Set.univproof · cited by 3,945
mul_oneproof · cited by 3,885
LE.le.transproof · cited by 3,151
iInfstatement and proof · cited by 1,690
Filter.univ_mem'proof · cited by 1,672

Cited by2

Results whose statement or proof uses this declaration.

ProbabilityTheory.IsRatCondKernelCDFAux.iInf_rat_gt_eqproof · cited by 1
ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gtproof · cited by 1