Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.integral_toSignedMeasure

∀ {X : Type u_2} {G : Type u_6} {mX : MeasurableSpace X} [inst : NormedAddCommGroup G] [inst_1 : NormedSpace ℝ G]
  {μ : MeasureTheory.Measure X} [inst_2 : MeasureTheory.IsFiniteMeasure μ] {f : X → G},
  ∫ᵛ (x : X), f x ∂<•μ.toSignedMeasure = ∫ (x : X), f x ∂μ

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

1 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.IsFiniteMeasure