Theorems · Theorem · probability
ProbabilityTheory.IndepFun.hasLaw_add
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {P : MeasureTheory.Measure Ω} {M : Type u_3} [inst : AddMonoid M]
{mM : MeasurableSpace M} [MeasurableAdd₂ M] {μ ν : MeasureTheory.Measure M} [MeasureTheory.SigmaFinite μ]
[MeasureTheory.SigmaFinite ν] {X Y : Ω → M},
ProbabilityTheory.HasLaw X μ P →
ProbabilityTheory.HasLaw Y ν P → ProbabilityTheory.IndepFun X Y P → ProbabilityTheory.HasLaw (X + Y) (μ.conv ν) P- Defined in
- Mathlib.Probability.HasLaw
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 224 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.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- AddMonoidstatement and proof · cited by 2,864
- MeasureTheory.Measure.mapproof · cited by 858
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- ProbabilityTheory.IndepFunstatement and proof · cited by 192
- MeasurableAdd₂statement and proof · cited by 155
- ProbabilityTheory.HasLawstatement and proof · cited by 69
- MeasureTheory.Measure.convstatement and proof · cited by 41
- ProbabilityTheory.HasLaw.map_eqproof · cited by 31
- ProbabilityTheory.HasLaw.aemeasurableproof · cited by 24
- AEMeasurable.addproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IndepFun.hasLaw_add_poissonMeasureproof · cited by 0
- ProbabilityTheory.IndepFun.hasLaw_fun_addproof · cited by 0
- ProbabilityTheory.IndepFun.hasLaw_add_map_cast_poissonMeasureproof · cited by 0