Theorems · Theorem · functional analysis

SchwartzMap.coe_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 : MeasureTheory.MeasureSpace E] [inst_5 : BorelSpace E]
  [inst_6 : SecondCountableTopology E] [inst_7 : MeasureTheory.volume.HasTemperateGrowth] (f : SchwartzMap E F)
  (g : SchwartzMap E ℂ), ((SchwartzMap.toTemperedDistributionCLM E F MeasureTheory.volume) f) g = ∫ (x : E), g x • f x

Defined in: Mathlib.Analysis.Distribution.TemperedDistribution
Cited by: 0 results in Mathlib
Foundations: Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace NormedAddCommGroup NormedSpace MeasureTheory.MeasureSpace BorelSpace SecondCountableTopology MeasureTheory.Measure.HasTemperateGrowth

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MeasureTheory.integralstatement · cited by 1,779

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