AbsolutelyContinuousOnInterval.exists_bound

∀ {F : Type u_2} [inst : SeminormedAddCommGroup F] {a b : ℝ} {f : ℝ → F},
  AbsolutelyContinuousOnInterval f a b → ∃ C, ∀ x ∈ Set.uIcc a b, ‖f x‖ ≤ C

If f is absolutely continuous on uIcc a b, then f is bounded on uIcc a b.

Defined in: Mathlib.MeasureTheory.Function.AbsolutelyContinuous
Cited by: 1 results in Mathlib
Foundations: Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SeminormedAddCommGroup

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.