Theorems · Theorem · measure theory

intervalIntegral.norm_integral_eq_norm_integral_uIoc

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

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

5 results in Mathlib

Foundations

Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace