Theorems · Theorem · measure theory

MeasureTheory.integrableOn_Iic_iff_integrableAtFilter_atBot

∀ {X : Type u_1} {ε : Type u_3} [inst : MeasurableSpace X] [inst_1 : TopologicalSpace X] [inst_2 : TopologicalSpace ε]
  [inst_3 : ContinuousENorm ε] {f : X → ε} {μ : MeasureTheory.Measure X} [TopologicalSpace.PseudoMetrizableSpace ε]
  {a : X} [inst_5 : LinearOrder X] [CompactIccSpace X],
  MeasureTheory.IntegrableOn f (Set.Iic a) μ ↔
    MeasureTheory.IntegrableAtFilter f Filter.atBot μ ∧ MeasureTheory.LocallyIntegrableOn f (Set.Iic a) μ

Defined in

Mathlib.MeasureTheory.Function.LocallyIntegrable

Cited by

3 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceTopologicalSpaceTopologicalSpaceContinuousENormTopologicalSpace.PseudoMetrizableSpaceLinearOrderCompactIccSpace