Theorems · Theorem · functional analysis

TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq

∀ {E : Type u_3} {F : Type u_4} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
  [inst_3 : NormedSpace ℂ F] [inst_4 : MeasurableSpace E] [inst_5 : BorelSpace E] [inst_6 : SecondCountableTopology E]
  [inst_7 : FiniteDimensional ℝ E] {μ : MeasureTheory.Measure E} [inst_8 : μ.IsAddHaarMeasure] (f : SchwartzMap E F)
  (m : E),
  LineDeriv.lineDerivOp m ((SchwartzMap.toTemperedDistributionCLM E F μ) f) =
    (SchwartzMap.toTemperedDistributionCLM E F μ) (LineDeriv.lineDerivOp m f)

Defined in: Mathlib.Analysis.Distribution.TemperedDistribution
Cited by: 0 results in Mathlib
Foundations: Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace NormedAddCommGroup NormedSpace MeasurableSpace BorelSpace SecondCountableTopology FiniteDimensional MeasureTheory.Measure.IsAddHaarMeasure

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites28

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
RingHom.idstatement and proof · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpacestatement and proof · cited by 12,499
MeasureTheory.Measurestatement and proof · cited by 10,939
Set.Elemstatement · cited by 7,166
Set.ofPredstatement · cited by 6,101
Complexstatement and proof · cited by 5,565
ContinuousLinearMapstatement · cited by 5,352

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.