Theorems · Theorem · measure theory

MeasureTheory.integrable_indicator_iff

∀ {α : Type u_1} {ε' : Type u_4} {mα : MeasurableSpace α} {s : Set α} {μ : MeasureTheory.Measure α}
  [inst : TopologicalSpace ε'] [inst_1 : ESeminormedAddMonoid ε'] {f : α → ε'},
  MeasurableSet s → (MeasureTheory.Integrable (s.indicator f) μ ↔ MeasureTheory.IntegrableOn f s μ)

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

30 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceESeminormedAddMonoid