Theorems · Theorem · measure theory

intervalIntegrable_congr_codiscreteWithin

∀ {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} [MeasureTheory.NullSingletonClass μ],
  f =ᶠ[Filter.codiscreteWithin (Set.uIoc a b)] g → (IntervalIntegrable f μ a b ↔ IntervalIntegrable g μ a b)

Interval integrability is invariant when functions change along discrete sets.

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceENormedAddMonoidTopologicalSpace.PseudoMetrizableSpaceMeasureTheory.NullSingletonClass