Theorems · Theorem · measure theory

MeasureTheory.VectorMeasure.integral_dirac

∀ {X : Type u_2} {E : Type u_4} {F : Type u_5} {G : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : NormedAddCommGroup G] [inst_5 : NormedSpace ℝ G]
  {f : X → E} {B : E →L[ℝ] F →L[ℝ] G} [inst_6 : MeasurableSpace X] [MeasurableSingletonClass X] [CompleteSpace G]
  {a : X} {v : F}, ∫ᵛ (x : X), f x ∂[B; MeasureTheory.VectorMeasure.dirac a v] = (B (f a)) v

Defined in

Mathlib.MeasureTheory.VectorMeasure.Integral

Cited by

2 results in Mathlib

Foundations

Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceMeasurableSpaceMeasurableSingletonClassCompleteSpace