Theorems · Theorem · functional analysis

MeasureTheory.MemLp.of_bound

∀ {α : Type u_1} {E : Type u_4} {m0 : MeasurableSpace α} {p : ENNReal} {μ : MeasureTheory.Measure α}
  [inst : NormedAddCommGroup E] [MeasureTheory.IsFiniteMeasure μ] {f : α → E},
  MeasureTheory.AEStronglyMeasurable f μ → ∀ (C : ℝ), (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ C) → MeasureTheory.MemLp f p μ

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

NormedAddCommGroupMeasureTheory.IsFiniteMeasure