Theorems · Theorem · measure theory

MeasureTheory.Measure.ext_of_integral_eq_on_compactlySupported_nnreal

∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] [LocallyCompactSpace X] [inst_3 : MeasurableSpace X]
  [BorelSpace X] {μ ν : MeasureTheory.Measure X} [μ.Regular] [ν.Regular],
  (∀ (f : CompactlySupportedContinuousMap X NNReal), ∫ (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≥0), then they are equal.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.NNReal

Cited by

2 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceT2SpaceLocallyCompactSpaceMeasurableSpaceBorelSpaceMeasureTheory.Measure.RegularMeasureTheory.Measure.Regular