Theorems · Theorem · measure theory

MeasureTheory.Integrable.intervalIntegrable

∀ {ε : Type u_3} [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε] {f : ℝ → ε} {a b : ℝ}
  {μ : MeasureTheory.Measure ℝ}, MeasureTheory.Integrable f μ → IntervalIntegrable f μ a b

If a function is integrable with respect to a given measure μ then it is interval integrable with respect to μ on uIcc a b.

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

1 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoid