Theorems · Theorem · measure theory
MeasureTheory.measurable_lconvolution
∀ {G : Type u_1} {mG : MeasurableSpace G} [inst : Add G] [inst_1 : Neg G] [MeasurableAdd₂ G] [MeasurableNeg G]
{f g : G → ENNReal} (μ : MeasureTheory.Measure G) [MeasureTheory.SFinite μ],
Measurable f → Measurable g → Measurable (MeasureTheory.lconvolution f g μ)The convolution of measurable functions is measurable.
- Defined in
- Mathlib.Analysis.LConvolution
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.SFinitestatement and proof · cited by 449
- MeasurableAdd₂statement and proof · cited by 155
- measurable_id'proof · cited by 145
- MeasurableNegstatement and proof · cited by 130
- Measurable.fun_compproof · cited by 95
- Measurable.fstproof · cited by 51
- Measurable.sndproof · cited by 51
- Measurable.fun_mulproof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.HaveLebesgueDecomposition.convproof · cited by 2