Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.integral_eq_sum_filter

∀ {α : Type u_1} {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F]
  [inst_2 : DecidablePred fun x => x ≠ 0] {m : MeasurableSpace α} (f : MeasureTheory.SimpleFunc α F)
  (μ : MeasureTheory.Measure α),
  MeasureTheory.SimpleFunc.integral μ f = ∑ x ∈ f.range with x ≠ 0, μ.real (⇑f ⁻¹' {x}) • x

Defined in

Mathlib.MeasureTheory.Integral.Bochner.L1

Cited by

2 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceDecidablePred