Theorems · Theorem · probability
ProbabilityTheory.IndepFun.mul_hasPDF
∀ {Ω : Type u_1} {G : Type u_2} {mΩ : MeasurableSpace Ω} {ℙ : MeasureTheory.Measure Ω} [inst : Group G]
{mG : MeasurableSpace G} [MeasurableMul₂ G] [MeasurableInv G] {μ : MeasureTheory.Measure G} [μ.IsMulLeftInvariant]
{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
- Groupstatement and proof · cited by 6,238
- 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
- MeasurableMul₂statement and proof · cited by 139
- MeasureTheory.Measure.IsMulLeftInvariantstatement and proof · cited by 118
- MeasurableInvstatement and proof · cited by 98
- MeasureTheory.HasPDFstatement and proof · cited by 37
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