Theorems · Theorem · functional analysis

SchwartzMap.toTemperedDistributionCLM_apply_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 : MeasurableSpace E] [inst_5 : BorelSpace E] [inst_6 : SecondCountableTopology E]
  (μ : autoParam (MeasureTheory.Measure E) SchwartzMap.toTemperedDistributionCLM_apply_apply._auto_1)
  [hμ : μ.HasTemperateGrowth] (f : SchwartzMap E F) (g : SchwartzMap E ℂ),
  ((SchwartzMap.toTemperedDistributionCLM E F μ) f) g = ∫ (x : E), g x • f x ∂μ

Defined in

Mathlib.Analysis.Distribution.TemperedDistribution

Cited by

7 results in Mathlib

Foundations

Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceBorelSpaceSecondCountableTopologyMeasureTheory.Measure.HasTemperateGrowth