Theorems · Theorem · functional analysis

MeasureTheory.eLpNorm_le_of_ae_bound

∀ {α : Type u_1} {F : Type u_5} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup F] {f : α → F} {C : ℝ},
  (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ C) → MeasureTheory.eLpNorm f p μ ≤ μ Set.univ ^ p.toReal⁻¹ * ENNReal.ofReal C

Defined in

Mathlib.MeasureTheory.Function.LpSeminorm.Basic

Cited by

6 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup