Theorems · Theorem · measure theory

MeasureTheory.weightedSMul_add_measure

∀ {α : Type u_1} {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] {m : MeasurableSpace α}
  (μ ν : MeasureTheory.Measure α) {s : Set α},
  μ s ≠ ⊤ →
    ν s ≠ ⊤ → MeasureTheory.weightedSMul (μ + ν) s = MeasureTheory.weightedSMul μ s + MeasureTheory.weightedSMul ν s

Defined in

Mathlib.MeasureTheory.Integral.Bochner.L1

Cited by

1 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace