Theorems · Theorem · functional analysis

SchwartzMap.norm_toLp_one

∀ {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 : SecondCountableTopologyEither E F] {f : SchwartzMap E F} {μ : MeasureTheory.Measure E}
  [hμ : μ.HasTemperateGrowth], ‖f.toLp 1 μ‖ = ∫ (x : E), ‖f x‖ ∂μ

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceOpensMeasurableSpaceSecondCountableTopologyEitherMeasureTheory.Measure.HasTemperateGrowth