Theorems · Theorem · probability
ProbabilityTheory.iIndepFun.isProbabilityMeasure
∀ {Ω : Type u_1} {ι : Type u_2} {_mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {β : ι → Type u_10}
{m : (i : ι) → MeasurableSpace (β i)} {f : (i : ι) → Ω → β i},
ProbabilityTheory.iIndepFun f μ → MeasureTheory.IsProbabilityMeasure μ- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.univproof · cited by 3,945
- pow_zeroproof · cited by 1,094
- Set.iInterproof · cited by 1,084
- MeasureTheory.IsProbabilityMeasurestatement · cited by 392
- Set.iInter_congr_Propproof · cited by 170
- Finset.prod_constproof · cited by 154
- ProbabilityTheory.iIndepFunstatement and proof · cited by 138
- Set.iInter_univproof · cited by 24
- Set.iInter_of_emptyproof · cited by 23
Cited by14
Results whose statement or proof uses this declaration.
- ProbabilityTheory.iIndepFun.charFunDual_map_finsetSum_eq_prodproof · cited by 4
- ProbabilityTheory.iIndepFun.map_fun_eq_pi_mapproof · cited by 4
- ProbabilityTheory.iIndepFun.mgf_sum₀proof · cited by 3
- ProbabilityTheory.iIndepFun.hasGaussianLawproof · cited by 3
- ProbabilityTheory.iIndepFun.map_fun_eq_infinitePi_map₀proof · cited by 3
- ProbabilityTheory.HasIndepIncrements.natproof · cited by 2
- ProbabilityTheory.iIndepFun_uncurryproof · cited by 2
- ProbabilityTheory.iIndepFun.integral_fun_prod_compproof · cited by 2
- ProbabilityTheory.iIndepFun.hasLaw_infinitePiproof · cited by 1
- ProbabilityTheory.iIndepFun.cgf_sum₀proof · cited by 1
- ProbabilityTheory.iIndepFun.condExp_natural_ae_eq_of_ltproof · cited by 1
- ProbabilityTheory.cond_iInterproof · cited by 1