Theorems · Theorem · probability
ProbabilityTheory.exists_hasLaw_indepFun
∀ {ι : Type v} (𝓧 : ι → Type u) {m𝓧 : (i : ι) → MeasurableSpace (𝓧 i)} (μ : (i : ι) → MeasureTheory.Measure (𝓧 i))
[hμ : ∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)],
∃ Ω x P X,
(∀ (i : ι), Measurable (X i)) ∧
(∀ (i : ι), ProbabilityTheory.HasLaw (X i) (μ i) P) ∧
ProbabilityTheory.iIndepFun X P ∧ MeasureTheory.IsProbabilityMeasure P- Defined in
- Mathlib.Probability.HasLawExists
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Measurablestatement · cited by 1,499
- MeasureTheory.Measure.mapproof · cited by 858
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- Function.evalproof · cited by 140
- ProbabilityTheory.iIndepFunstatement · cited by 138
- measurable_pi_applyproof · cited by 77
- MeasureTheory.MeasurePreserving.map_eqproof · cited by 72
- ProbabilityTheory.HasLawstatement · cited by 69
- MeasureTheory.Measure.infinitePiproof · cited by 48
- MeasureTheory.Measure.map_id'proof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.exists_iidproof · cited by 0