Zulip Chat Archive

Stream: mathlib4

Topic: Organization of Multiplication of "Random Variables"


David Ledvinka (May 28 2025 at 13:56):

I am wondering where I should put the following theorems (and variations) in possibly one or multiple files.

theorem IndepFun.map_mul_eq_map_mconv_map [MeasurableMul₂ M]
    {f g : Ω  M} (hf : AEMeasurable f μ) (hg : AEMeasurable g μ) (hfg : IndepFun f g μ) :
    μ.map (f * g) = (μ.map f)  (μ.map g)

theorem mconv_withDensity_eq_mlconvolution {f g : G  0}
    (hf : AEMeasurable f π) (hg : AEMeasurable g π) :
    π.withDensity f  π.withDensity g = π.withDensity (f ⋆ₗ[π] g)

theorem IndepFun.map_mul_eq_pdf_mlconvolution {μ : Measure Ω} [IsFiniteMeasure μ]
     {f g : Ω  G} (hf : AEMeasurable f μ) (hg : AEMeasurable g μ)
    (hfg : IndepFun f g μ) [HasPDF f μ π] [HasPDF g μ π] :
    pdf (f * g) μ π =ᶠ[ae π] (pdf f μ π) ⋆ₗ[π] (pdf g μ π)

Yaël Dillies (May 28 2025 at 13:58):

What does #min_imports in before each of these say?

Ruben Van de Velde (May 28 2025 at 15:07):

TIL about #min_imports in

David Ledvinka (May 28 2025 at 16:40):

First one has min imports

import Mathlib.MeasureTheory.Group.Convolution
import Mathlib.Probability.Independence.Basic
import Init.Data.List.Nat.Pairwise

Second one has min imports

import Mathlib.Analysis.LConvolution
import Mathlib.MeasureTheory.Group.Convolution
import Mathlib.MeasureTheory.Measure.WithDensity
import Init.Data.List.Nat.Pairwise

Third one has min imports

import Mathlib.Analysis.LConvolution
import Mathlib.Probability.Density
import Mathlib.MeasureTheory.Group.Convolution
import Init.Data.List.Nat.Pairwise

Last updated: Dec 20 2025 at 21:32 UTC