Theorems · Theorem · measure theory

MeasureTheory.measure_smul_average

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

Defined in

Mathlib.MeasureTheory.Integral.Average

Cited by

4 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.IsFiniteMeasure