Theorems · Theorem · measure theory

NNRealRMK.integralLinearMap_inj

∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] [LocallyCompactSpace X] [inst_3 : MeasurableSpace X]
  [inst_4 : BorelSpace X] {μ ν : MeasureTheory.Measure X} [inst_5 : μ.Regular] [inst_6 : ν.Regular],
  CompactlySupportedContinuousMap.integralLinearMap μ = CompactlySupportedContinuousMap.integralLinearMap ν ↔ μ = ν

If two regular measures induce the same linear functional on C_c(X, ℝ≥0), then they are equal.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.NNReal

Cited by

0 results in Mathlib

Foundations

Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT2SpaceLocallyCompactSpaceMeasurableSpaceBorelSpaceMeasureTheory.Measure.RegularMeasureTheory.Measure.Regular