Theorems · Theorem · measure theory

MeasureTheory.IntegrableAtFilter.sup_iff

∀ {α : Type u_1} {ε' : Type u_4} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace ε']
  [inst_1 : ESeminormedAddMonoid ε'] [TopologicalSpace.PseudoMetrizableSpace ε'] {f : α → ε'} {l l' : Filter α},
  MeasureTheory.IntegrableAtFilter f (l ⊔ l') μ ↔
    MeasureTheory.IntegrableAtFilter f l μ ∧ MeasureTheory.IntegrableAtFilter f l' μ

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

1 results in Mathlib

Foundations

Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceESeminormedAddMonoidTopologicalSpace.PseudoMetrizableSpace