Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.setIntegral_toSignedMeasure

∀ {X : Type u_2} {G : Type u_5} {mX : MeasurableSpace X} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G]
  {μ : MeasureTheory.Measure X} [inst_2 : MeasureTheory.IsFiniteMeasure μ] {f : X → G} {s : Set X},
  MeasurableSet s → ∫ᵛ (x : X) in s, f x ∂<•μ.toSignedMeasure = ∫ (x : X) in s, f x ∂μ

Defined in

Mathlib.MeasureTheory.VectorMeasure.SetIntegral

Cited by

1 results in Mathlib

Foundations

Depth 253 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.IsFiniteMeasure