Theorems · Theorem · measure theory

intervalIntegral.integral_congr_ae_restrict

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} {f g : ℝ → E}
  {μ : MeasureTheory.Measure ℝ},
  f =ᵐ[μ.restrict (Set.uIoc a b)] g → ∫ (x : ℝ) in a..b, f x ∂μ = ∫ (x : ℝ) in a..b, g x ∂μ

Integrals are equal for functions that agree almost everywhere for the restricted measure.

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

6 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace