Theorems · Theorem · functional analysis

MeasureTheory.Lp.toTemperedDistribution_toLp_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 : CompleteSpace F] [inst_5 : MeasurableSpace E] [inst_6 : BorelSpace E]
  {μ : MeasureTheory.Measure E} [hμ : μ.HasTemperateGrowth] [inst_7 : SecondCountableTopology E] {p : ENNReal}
  [hp : Fact (1 ≤ p)] (f : SchwartzMap E F),
  MeasureTheory.Lp.toTemperedDistribution (f.toLp p μ) = (SchwartzMap.toTemperedDistributionCLM E F μ) f

Defined in

Mathlib.Analysis.Distribution.TemperedDistribution

Cited by

2 results in Mathlib

Foundations

Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpaceMeasurableSpaceBorelSpaceMeasureTheory.Measure.HasTemperateGrowthSecondCountableTopologyFact