Theorems · Theorem · measure theory

MeasureTheory.integral_singleton

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

Defined in

Mathlib.MeasureTheory.Integral.Bochner.Basic

Cited by

3 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceMeasurableSingletonClass