Theorems · Theorem · measure theory

MeasureTheory.MemLp.integrable_enorm_pow

∀ {α : Type u_1} {ε : Type u_5} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace ε]
  [inst_1 : ContinuousENorm ε] {f : α → ε} {p : ℕ},
  MeasureTheory.MemLp f (↑p) μ → p ≠ 0 → MeasureTheory.Integrable (fun x => ‖f x‖ₑ ^ p) μ

Defined in

Mathlib.MeasureTheory.Function.L1Space.Integrable

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceContinuousENorm