Theorems · Theorem · measure theory

MeasureTheory.mconv_withDensity_eq_mlconvolution

∀ {G : Type u_3} [inst : Group G] {mG : MeasurableSpace G} [MeasurableMul₂ G] [MeasurableInv G]
  {μ : MeasureTheory.Measure G} [MeasureTheory.SFinite μ] [μ.IsMulLeftInvariant] {f g : G → ENNReal},
  Measurable f →
    Measurable g → (μ.withDensity f).mconv (μ.withDensity g) = μ.withDensity (MeasureTheory.mlconvolution f g μ)

Defined in: Mathlib.MeasureTheory.Measure.WithDensity
Cited by: 1 results in Mathlib
Foundations: Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Group MeasurableMul₂ MeasurableInv MeasureTheory.SFinite MeasureTheory.Measure.IsMulLeftInvariant

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Cites14

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
Measurablestatement and proof · cited by 1,499
MeasureTheory.SFinitestatement and proof · cited by 449
Measurable.aemeasurableproof · cited by 304
MeasureTheory.Measure.withDensitystatement · cited by 265
MeasurableMul₂statement and proof · cited by 139
MeasureTheory.Measure.IsMulLeftInvariantstatement and proof · cited by 118
MeasurableInvstatement and proof · cited by 98
MeasureTheory.Measure.mconvstatement · cited by 31

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.mconv_eq_withDensity_mlconvolution_rnDerivproof · cited by 3