Theorems · Theorem · measure theory
MeasureTheory.aemeasurable_lconvolution
∀ {G : Type u_1} {mG : MeasurableSpace G} [inst : AddGroup G] [MeasurableAdd₂ G] [MeasurableNeg G]
{μ : MeasureTheory.Measure G} [μ.IsAddLeftInvariant] [MeasureTheory.SFinite μ] {f g : G → ENNReal},
AEMeasurable f μ → AEMeasurable g μ → AEMeasurable (MeasureTheory.lconvolution f g μ) μThe convolution of AEMeasurable functions is AEMeasurable.
- Defined in
- Mathlib.Analysis.LConvolution
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- AEMeasurablestatement and proof · cited by 840
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasureTheory.Measure.prodproof · cited by 353
- MeasurableAdd₂statement and proof · cited by 155
- MeasureTheory.Measure.IsAddLeftInvariantstatement and proof · cited by 148
- MeasurableNegstatement and proof · cited by 130
- AEMeasurable.comp_quasiMeasurePreservingproof · cited by 17
- MeasureTheory.lconvolutionstatement · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.rnDeriv_convproof · cited by 1
- MeasureTheory.rnDeriv_conv'proof · cited by 1
- MeasureTheory.conv_withDensity_eq_mlconvolution₀proof · cited by 1