Theorems · Theorem · measure theory

MeasureTheory.Integrable.integral_smul

∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G] {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} {R : Type u_6} [inst_2 : NormedRing R] [inst_3 : Module R G] [IsBoundedSMul R G]
  [SMulCommClass ℝ R G] (c : R) {f : α → G},
  MeasureTheory.Integrable f μ → ∫ (a : α), c • f a ∂μ = c • ∫ (a : α), f a ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceNormedRingModuleIsBoundedSMulSMulCommClass