Theorems · Theorem · probability
ProbabilityTheory.IndepFun.add_hasPDF
∀ {Ω : Type u_1} {G : Type u_2} {mΩ : MeasurableSpace Ω} {ℙ : MeasureTheory.Measure Ω} [inst : AddGroup G]
{mG : MeasurableSpace G} [MeasurableAdd₂ G] [MeasurableNeg G] {μ : MeasureTheory.Measure G} [μ.IsAddLeftInvariant]
{X Y : Ω → G} [MeasureTheory.SFinite μ] [MeasureTheory.HasPDF X ℙ μ] [MeasureTheory.HasPDF Y ℙ μ]
[MeasureTheory.IsFiniteMeasure ℙ], ProbabilityTheory.IndepFun X Y ℙ → MeasureTheory.HasPDF (X + Y) ℙ μ- Defined in
- Mathlib.Probability.Density
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 235 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- AddGroupstatement and proof · cited by 4,410
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.Measure.mapproof · cited by 858
- MeasureTheory.SigmaFiniteproof · cited by 526
- MeasureTheory.SFinitestatement and proof · cited by 449
- ProbabilityTheory.IndepFunstatement and proof · cited by 192
- MeasurableAdd₂statement and proof · cited by 155
- MeasureTheory.Measure.IsAddLeftInvariantstatement and proof · cited by 148
- MeasurableNegstatement and proof · cited by 130
- MeasureTheory.HasPDFstatement and proof · cited by 37
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