Theorems · Theorem · measure theory

intervalIntegrable_iff_integrableOn_Ico_of_le

∀ {ε : Type u_3} [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε] [TopologicalSpace.PseudoMetrizableSpace ε]
  {f : ℝ → ε} {a b : ℝ} {μ : MeasureTheory.Measure ℝ} [MeasureTheory.NullSingletonClass μ],
  a ≤ b →
    autoParam (‖f a‖ₑ ≠ ⊤) intervalIntegrable_iff_integrableOn_Ico_of_le._auto_1 →
      autoParam (‖f b‖ₑ ≠ ⊤) intervalIntegrable_iff_integrableOn_Ico_of_le._auto_3 →
        (IntervalIntegrable f μ a b ↔ MeasureTheory.IntegrableOn f (Set.Ico a b) μ)

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpaceMeasureTheory.NullSingletonClass