Theorems · Theorem · measure theory

MeasureTheory.Integrable.of_bound

∀ {α : Type u_1} {E : Type u_5} {mα : MeasurableSpace α} [inst : NormedAddCommGroup E] {μ : MeasureTheory.Measure α}
  [MeasureTheory.IsFiniteMeasure μ] {f : α → E},
  MeasureTheory.AEStronglyMeasurable f μ → ∀ (C : ℝ), (∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ C) → MeasureTheory.Integrable f μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

6 results in Mathlib

Foundations

Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupMeasureTheory.IsFiniteMeasure