Theorems · Theorem · measure theory

MeasureTheory.integrableOn_iff_integrable_of_support_subset

∀ {α : Type u_1} {mα : MeasurableSpace α} {s : Set α} {μ : MeasureTheory.Measure α} {ε' : Type u_7}
  [inst : TopologicalSpace ε'] [inst_1 : ENormedAddMonoid ε'] [TopologicalSpace.PseudoMetrizableSpace ε'] {f : α → ε'},
  Function.support f ⊆ s → (MeasureTheory.IntegrableOn f s μ ↔ MeasureTheory.Integrable f μ)

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

10 results in Mathlib

Foundations

Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpace