Theorems · Theorem · measure theory

interval_average_eq

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] (f : ℝ → E) (a b : ℝ),
  ⨍ (x : ℝ) in a..b, f x = (b - a)⁻¹ • ∫ (x : ℝ) in a..b, f x

Defined in

Mathlib.MeasureTheory.Integral.IntervalAverage

Cited by

3 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpace