Theorems · Theorem · functional analysis

SchwartzMap.toLpCLM_apply

∀ {𝕜 : Type u_2} {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : MeasurableSpace E]
  [inst_5 : OpensMeasurableSpace E] [inst_6 : NormedField 𝕜] [inst_7 : NormedSpace 𝕜 F] [inst_8 : SMulCommClass ℝ 𝕜 F]
  [inst_9 : SecondCountableTopologyEither E F] {p : ENNReal} [inst_10 : Fact (1 ≤ p)] {μ : MeasureTheory.Measure E}
  [hμ : μ.HasTemperateGrowth] {f : SchwartzMap E F}, (SchwartzMap.toLpCLM 𝕜 F p μ) f = f.toLp p μ

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

0 results in Mathlib

Foundations

Depth 236 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceOpensMeasurableSpaceNormedFieldNormedSpaceSMulCommClassSecondCountableTopologyEitherFactMeasureTheory.Measure.HasTemperateGrowth