Theorems · Theorem · functional analysis

MeasureTheory.Lp.dist_eq_eLpNorm_neg_add

∀ {α : Type u_1} {E : Type u_4} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] (f g : ↥(MeasureTheory.Lp E p μ)),
  dist f g = (MeasureTheory.eLpNorm (-↑↑f + ↑↑g) p μ).toReal

Defined in

Mathlib.MeasureTheory.Function.LpSpace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup