Theorems · Theorem · measure theory

MeasureTheory.integral_smul_measure

∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G] {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} (f : α → G) (c : ENNReal), ∫ (x : α), f x ∂c • μ = c.toReal • ∫ (x : α), f x ∂μ

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

22 results in Mathlib

Foundations

Depth 252 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace