Theorems · Theorem · measure theory

MeasureTheory.Measure.exists_regular_eq_of_compactSpace

∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] [inst_2 : MeasurableSpace X] [BorelSpace X] [CompactSpace X]
  (μ : MeasureTheory.Measure X) [MeasureTheory.IsFiniteMeasure μ],
  ∃ ν,
    ν.Regular ∧
      MeasureTheory.IsFiniteMeasure ν ∧ ∀ (g : BoundedContinuousFunction X ℝ), ∫ (x : X), g x ∂μ = ∫ (x : X), g x ∂ν

Given a finite measure on a compact space, there exists another finite measure which integrates in the same way bounded continuous functions, and is regular.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real

Cited by

1 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceT2SpaceMeasurableSpaceBorelSpaceCompactSpaceMeasureTheory.IsFiniteMeasure