Theorems · Definition · functional analysis

MeasureTheory.Lp.toTemperedDistributionCLM

{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] →
            [CompleteSpace F] →
              [inst_5 : MeasurableSpace E] →
                [BorelSpace E] →
                  (μ : autoParam (MeasureTheory.Measure E) MeasureTheory.Lp.toTemperedDistributionCLM._auto_1) →
                    [μ.HasTemperateGrowth] →
                      (p : ENNReal) → [hp : Fact (1 ≤ p)] → ↥(MeasureTheory.Lp F p μ) →L[ℂ] TemperedDistribution E F

The natural embedding of L^p into tempered distributions.

Defined in

Mathlib.Analysis.Distribution.TemperedDistribution

Cited by

9 results in Mathlib

Foundations

Depth 244 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpaceMeasurableSpaceBorelSpaceMeasureTheory.Measure.HasTemperateGrowthFact