Theorems · Theorem · measure theory

intervalIntegrable_const_iff

∀ {ε : Type u_3} [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε] [TopologicalSpace.PseudoMetrizableSpace ε]
  {a b : ℝ} {μ : MeasureTheory.Measure ℝ} {c : ε},
  autoParam (‖c‖ₑ ≠ ⊤) intervalIntegrable_const_iff._auto_1 →
    (IntervalIntegrable (fun x => c) μ a b ↔ c = 0 ∨ μ (Set.uIoc a b) < ⊤)

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

4 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpace