Theorems · Theorem · functional analysis

MeasureTheory.eLpNorm_eq_zero_iff

∀ {α : Type u_1} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} {ε : Type u_7}
  [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε] {f : α → ε},
  MeasureTheory.AEStronglyMeasurable f μ → p ≠ 0 → (MeasureTheory.eLpNorm f p μ = 0 ↔ f =ᵐ[μ] 0)

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Basic

Cited by

5 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoid