Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.setIntegral_dirac

∀ {X : Type u_2} {E : Type u_3} {F : Type u_4} {G : Type u_5} [inst : NormedAddCommGroup E]
  [inst_1 : NormedAddCommGroup F] [inst_2 : NormedAddCommGroup G] {f : X → E} [inst_3 : NormedSpace ℝ E]
  [inst_4 : NormedSpace ℝ F] [inst_5 : NormedSpace ℝ G] {B : E →L[ℝ] F →L[ℝ] G} [inst_6 : MeasurableSpace X]
  [MeasurableSingletonClass X] [CompleteSpace G] {a : X} {v : F} {s : Set X},
  MeasurableSet s →
    ∀ [inst_9 : Decidable (a ∈ s)],
      ∫ᵛ (x : X) in s, f x ∂[B; MeasureTheory.VectorMeasure.dirac a v] = if a ∈ s then (B (f a)) v else 0

Defined in

Mathlib.MeasureTheory.VectorMeasure.SetIntegral

Cited by

0 results in Mathlib

Foundations

Depth 248 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedAddCommGroupNormedAddCommGroupNormedSpaceNormedSpaceNormedSpaceMeasurableSpaceMeasurableSingletonClassCompleteSpaceDecidable