Theorems · Theorem · measure theory

intervalIntegral.integral_congr

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

If two functions are equal in the relevant interval, their interval integrals are also equal.

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

18 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace