Theorems · Theorem · measure theory

MeasureTheory.integral_dirac

∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [hE : CompleteSpace E]
  [inst_2 : MeasurableSpace α] [MeasurableSingletonClass α] (f : α → E) (a : α),
  ∫ (x : α), f x ∂MeasureTheory.Measure.dirac a = f a

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

20 results in Mathlib

Foundations

Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceMeasurableSpaceMeasurableSingletonClass