Theorems · Theorem · probability

MeasureTheory.Measure.IsCondKernel.isProbabilityMeasure

∀ {α : Type u_1} {Ω : Type u_3} {mα : MeasurableSpace α} {mΩ : MeasurableSpace Ω} (ρ : MeasureTheory.Measure (α × Ω))
  (ρCond : ProbabilityTheory.Kernel α Ω) [ρ.IsCondKernel ρCond] [MeasureTheory.IsFiniteMeasure ρ]
  [MeasurableSingletonClass α] {a : α}, ρ.fst {a} ≠ 0 → MeasureTheory.IsProbabilityMeasure (ρCond a)

Defined in: Mathlib.Probability.Kernel.Disintegration.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.Measure.IsCondKernel MeasureTheory.IsFiniteMeasure MeasurableSingletonClass

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Cites18

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
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Set.univproof · cited by 3,945
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
MeasureTheory.IsProbabilityMeasurestatement · cited by 392
MeasurableSingletonClassstatement and proof · cited by 230
MeasureTheory.measure_ne_topproof · cited by 171
MeasureTheory.Measure.fststatement and proof · cited by 70

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.Measure.IsCondKernel.isMarkovKernelproof · cited by 0