Theorems · Theorem · measure theory

RealRMK.integral_rieszMeasure

∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : T2Space X] [inst_2 : MeasurableSpace X] [inst_3 : BorelSpace X]
  (Λ : CompactlySupportedContinuousMap X ℝ →ₚ[ℝ] ℝ) [inst_4 : LocallyCompactSpace X]
  (f : CompactlySupportedContinuousMap X ℝ), ∫ (x : X), f x ∂ RealRMK.rieszMeasure Λ = Λ f

The Riesz-Markov-Kakutani representation theorem: given a positive linear functional Λ, the integral of f with respect to the rieszMeasure associated to Λ is equal to Λ f.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real

Cited by

7 results in Mathlib

Foundations

Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT2SpaceMeasurableSpaceBorelSpaceLocallyCompactSpace