Theorems · Theorem · functional analysis

MeasureTheory.Lp.nnnorm_eq_zero_iff

∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] {f : ↥(MeasureTheory.Lp E p μ)}, 0 < p → (‖f‖₊ = 0 ↔ f = 0)

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

1 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup