Theorems · Theorem · probability
ProbabilityTheory.Kernel.exists_measurable_map_eq_unitInterval
∀ {X : Type u_1} {Y : Type u_2} {mX : MeasurableSpace X} [Nonempty Y] {mY : MeasurableSpace Y} [StandardBorelSpace Y]
(κ : ProbabilityTheory.Kernel X Y) [ProbabilityTheory.IsMarkovKernel κ],
∃ f, Measurable (Function.uncurry f) ∧ ∀ (a : X), MeasureTheory.Measure.map (f a) MeasureTheory.volume = κ a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 273 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
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 · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.Elemstatement and proof · cited by 7,166
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.MeasureSpace.volumestatement and proof · cited by 1,323
- ProbabilityTheory.Kernelstatement and proof · cited by 1,281
- MeasureTheory.Measure.mapstatement and proof · cited by 858
- unitIntervalstatement and proof · cited by 607
- StandardBorelSpacestatement and proof · cited by 304
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.exists_measurable_map_eqproof · cited by 0