Theorems · Theorem · functional analysis

MeasureTheory.memLp_norm_iff

∀ {α : Type u_1} {E : Type u_4} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] {f : α → E},
  MeasureTheory.AEStronglyMeasurable f μ → (MeasureTheory.MemLp (fun x => ‖f x‖) p μ ↔ MeasureTheory.MemLp f p μ)

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Basic

Cited by

1 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup