Theorems · Theorem · measure theory

intervalIntegral.integral_interval_sub_interval_comm

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b c d : ℝ} {f : ℝ → E}
  {μ : MeasureTheory.Measure ℝ},
  IntervalIntegrable f μ a b →
    IntervalIntegrable f μ c d →
      IntervalIntegrable f μ a c →
        ∫ (x : ℝ) in a..b, f x ∂μ - ∫ (x : ℝ) in c..d, f x ∂μ = ∫ (x : ℝ) in a..c, f x ∂μ - ∫ (x : ℝ) in b..d, f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

2 results in Mathlib

Foundations

Depth 258 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace