Theorems · Theorem · measure theory

MeasureTheory.HasFiniteIntegral.restrict_of_bounded

∀ {α : Type u_1} {E : Type u_5} {mα : MeasurableSpace α} [inst : NormedAddCommGroup E] {f : α → E} {s : Set α}
  {μ : MeasureTheory.Measure α} (C : ℝ),
  μ s < ⊤ → (∀ᵐ (x : α) ∂μ.restrict s, ‖f x‖ ≤ C) → MeasureTheory.HasFiniteIntegral f (μ.restrict s)

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

3 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroup