Theorems · Theorem · measure theory

MeasureTheory.setAverage_eq

∀ {α : Type u_1} {E : Type u_2} {m0 : MeasurableSpace α} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  (μ : MeasureTheory.Measure α) (f : α → E) (s : Set α), ⨍ (x : α) in s, f x ∂μ = (μ.real s)⁻¹ • ∫ (x : α) in s, f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Average

Cited by

5 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpace