Theorems · Theorem · measure theory

intervalIntegrable_congr_ae

∀ {ε : Type u_3} [inst : TopologicalSpace ε] [inst_1 : ENormedAddMonoid ε] [TopologicalSpace.PseudoMetrizableSpace ε]
  {f : ℝ → ε} {a b : ℝ} {μ : MeasureTheory.Measure ℝ} {g : ℝ → ε},
  f =ᵐ[μ.restrict (Set.uIoc a b)] g → (IntervalIntegrable f μ a b ↔ IntervalIntegrable g μ a b)

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

3 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpace