Theorems · Theorem · functional analysis

MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : MeasurableSpace E] (p : ENNReal) {μ : MeasureTheory.Measure E},
  μ.HasTemperateGrowth → ∃ k, MeasureTheory.eLpNorm (fun x => (1 + ‖x‖) ^ (-↑k)) p μ < ⊤

For any HasTemperateGrowth measure and p, there exists an integer power k such that (1 + ‖x‖) ^ (-k) is in L^p.

Defined in

Mathlib.Analysis.Distribution.TemperateGrowth

Cited by

1 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupMeasurableSpace