Theorems · Theorem · measure theory

MeasureTheory.conv_withDensity_eq_lconvolution

∀ {G : Type u_3} [inst : AddGroup G] {mG : MeasurableSpace G} [MeasurableAdd₂ G] [MeasurableNeg G]
  {μ : MeasureTheory.Measure G} [MeasureTheory.SFinite μ] [μ.IsAddLeftInvariant] {f g : G → ENNReal},
  Measurable f →
    Measurable g → (μ.withDensity f).conv (μ.withDensity g) = μ.withDensity (MeasureTheory.lconvolution 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: AddGroup MeasurableAdd₂ MeasurableNeg MeasureTheory.SFinite MeasureTheory.Measure.IsAddLeftInvariant

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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
AddGroupstatement and proof · cited by 4,410
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
MeasurableAdd₂statement and proof · cited by 155
MeasureTheory.Measure.IsAddLeftInvariantstatement and proof · cited by 148
MeasurableNegstatement and proof · cited by 130
MeasureTheory.Measure.convstatement · cited by 41

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.conv_eq_withDensity_lconvolution_rnDerivproof · cited by 3