Theorems · Theorem · measure theory

integrableOn_Icc_iff_integrableOn_Ico

∀ {α : Type u_1} {ε' : Type u_4} {mα : MeasurableSpace α} [inst : PartialOrder α] [MeasurableSingletonClass α]
  [inst_2 : TopologicalSpace ε'] [inst_3 : ESeminormedAddMonoid ε'] [TopologicalSpace.PseudoMetrizableSpace ε']
  {f : α → ε'} {μ : MeasureTheory.Measure α} {a b : α} [MeasureTheory.NullSingletonClass μ],
  autoParam (‖f b‖ₑ ≠ ⊤) integrableOn_Icc_iff_integrableOn_Ico._auto_1 →
    (MeasureTheory.IntegrableOn f (Set.Icc a b) μ ↔ MeasureTheory.IntegrableOn f (Set.Ico a b) μ)

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

1 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderMeasurableSingletonClassTopologicalSpaceESeminormedAddMonoidTopologicalSpace.PseudoMetrizableSpaceMeasureTheory.NullSingletonClass