Theorems · Theorem · functional analysis

MeasureTheory.eLpNorm_ofReal

∀ {α : Type u_1} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α} (f : α → ℝ),
  (∀ᵐ (x : α) ∂μ, 0 ≤ f x) → MeasureTheory.eLpNorm (ENNReal.ofReal ∘ f) p μ = MeasureTheory.eLpNorm f p μ

f : α → ℝ and ENNReal.ofReal ∘ f : α → ℝ≥0∞ have the same eLpNorm. Usually, you should not use this lemma (but use enorms everywhere.)

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Basic

Cited by

1 results in Mathlib

Foundations

Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound