Theorems · Theorem · measure theory

NNRealRMK.rieszMeasure_integralLinearMap

∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : T2Space X] [inst_2 : LocallyCompactSpace X]
  [inst_3 : MeasurableSpace X] [inst_4 : BorelSpace X] {μ : MeasureTheory.Measure X} [inst_5 : μ.Regular],
  NNRealRMK.rieszMeasure (CompactlySupportedContinuousMap.integralLinearMap μ) = μ

Every regular measure is induced by a positive linear functional on C_c(X, ℝ≥0). That is, NNRealRMK.rieszMeasure is a surjective function onto regular measures.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.NNReal

Cited by

0 results in Mathlib

Foundations

Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT2SpaceLocallyCompactSpaceMeasurableSpaceBorelSpaceMeasureTheory.Measure.Regular