Theorems · Theorem · measure theory

MeasureTheory.Measure.ext_of_integral_eq_on_compactlySupported

∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] [inst_2 : MeasurableSpace X] [BorelSpace X]
  {μ ν : MeasureTheory.Measure X} [LocallyCompactSpace X] [μ.Regular] [ν.Regular],
  (∀ (f : CompactlySupportedContinuousMap X ℝ), ∫ (x : X), f x ∂μ = ∫ (x : X), f x ∂ν) → μ = ν

If two regular measures give the same integral for every function in C_c(X, ℝ), then they are equal.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real

Cited by

3 results in Mathlib

Foundations

Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT2SpaceMeasurableSpaceBorelSpaceLocallyCompactSpaceMeasureTheory.Measure.RegularMeasureTheory.Measure.Regular