Theorems · Theorem · abstract harmonic analysis
MeasureTheory.convolution_mul_swap
∀ {𝕜 : Type u𝕜} {G : Type uG} {x : G} [inst : NontriviallyNormedField 𝕜] [inst_1 : MeasurableSpace G]
{μ : MeasureTheory.Measure G} [inst_2 : AddCommGroup G] [μ.IsAddLeftInvariant] [μ.IsNegInvariant] [MeasurableNeg G]
[MeasurableAdd G] [inst_7 : NormedSpace ℝ 𝕜] {f g : G → 𝕜},
MeasureTheory.convolution f g (ContinuousLinearMap.mul 𝕜 𝕜) μ x = ∫ (t : G), f (x - t) * g t ∂μThe symmetric definition of convolution where the bilinear operator is multiplication.
- Defined in
- Mathlib.Analysis.Convolution
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommGroupstatement and proof · cited by 12,871
- NormedSpacestatement and proof · cited by 12,499
- MeasureTheory.Measurestatement and proof · cited by 10,939
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.Measure.IsAddLeftInvariantstatement and proof · cited by 148
- MeasurableNegstatement and proof · cited by 130
- MeasurableAddstatement and proof · cited by 78
- MeasureTheory.convolutionstatement · cited by 65
- ContinuousLinearMap.mulstatement and proof · cited by 63
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