Theorems · Theorem · functional analysis

SchwartzMap.integrable_pow_mul

∀ {D : Type u_4} {V : Type u_9} [inst : NormedAddCommGroup D] [inst_1 : NormedSpace ℝ D] [inst_2 : NormedAddCommGroup V]
  [inst_3 : NormedSpace ℝ V] [inst_4 : MeasurableSpace D] (μ : MeasureTheory.Measure D) [hμ : μ.HasTemperateGrowth]
  [BorelSpace D] [SecondCountableTopology D] (f : SchwartzMap D V) (k : ℕ),
  MeasureTheory.Integrable (fun x => ‖x‖ ^ k * ‖f x‖) μ

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceMeasureTheory.Measure.HasTemperateGrowthBorelSpaceSecondCountableTopology