Theorems · Theorem · probability
ProbabilityTheory.IndepFun.pdf_mul_eq_mlconvolution_pdf
∀ {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.pdf (X * Y) ℙ μ =ᵐ[μ]
MeasureTheory.mlconvolution (MeasureTheory.pdf X ℙ μ) (MeasureTheory.pdf Y ℙ μ) 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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Cites20
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
- ENNRealstatement and proof · cited by 9,879
- Groupstatement and proof · cited by 6,238
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasureTheory.Measure.rnDerivproof · cited by 234
- ProbabilityTheory.IndepFunstatement and proof · cited by 192
- MeasurableMul₂statement and proof · cited by 139
- MeasureTheory.Measure.IsMulLeftInvariantstatement and proof · cited by 118
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