Theorems · Theorem · measure theory

MeasureTheory.integral_eq_setToFun

∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} (f : α → E),
  ∫ (a : α), f a ∂μ = MeasureTheory.setToFun μ (MeasureTheory.weightedSMul μ) ⋯ f

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

31 results in Mathlib

Foundations

Depth 251 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace