Theorems · Theorem · measure theory

MeasureTheory.integrableOn_const_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'] {C : ε'},
  autoParam (‖C‖ₑ ≠ ⊤) MeasureTheory.integrableOn_const_iff._auto_1 →
    (MeasureTheory.IntegrableOn (fun x => C) s μ ↔ ‖C‖ₑ = 0 ∨ μ s < ⊤)

Defined in

Mathlib.MeasureTheory.Integral.IntegrableOn

Cited by

7 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceESeminormedAddMonoid