Theorems · Theorem · functional analysis

MeasureTheory.Lp.toTemperedDistribution_apply

∀ {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] {p : ENNReal} [hp : Fact (1 ≤ p)]
  (f : ↥(MeasureTheory.Lp F p μ)) (g : SchwartzMap E ℂ),
  (MeasureTheory.Lp.toTemperedDistribution f) g = ∫ (x : E), g x • ↑↑f x ∂μ

Defined in

Mathlib.Analysis.Distribution.TemperedDistribution

Cited by

3 results in Mathlib

Foundations

Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpaceMeasurableSpaceBorelSpaceMeasureTheory.Measure.HasTemperateGrowthFact