Theorems · Theorem · measure theory

MeasureTheory.lpNorm_eq_integral_norm_rpow_toReal

∀ {α : Type u_1} {E : Type u_2} {m : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] {f : α → E},
  p ≠ 0 →
    p ≠ ⊤ →
      MeasureTheory.AEStronglyMeasurable f μ →
        MeasureTheory.lpNorm f p μ = (∫ (x : α), ‖f x‖ ^ p.toReal ∂μ) ^ p.toReal⁻¹

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.LpNorm

Cited by

3 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup