Theorems · Theorem · measure theory

RealRMK.rieszMeasure_le_of_eq_one

∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : T2Space X] [inst_2 : MeasurableSpace X] [inst_3 : BorelSpace X]
  (Λ : CompactlySupportedContinuousMap X ℝ →ₚ[ℝ] ℝ) [inst_4 : LocallyCompactSpace X]
  {f : CompactlySupportedContinuousMap X ℝ},
  (∀ (x : X), 0 ≤ f x) →
    ∀ {K : Set X}, IsCompact K → (∀ x ∈ K, f x = 1) → (RealRMK.rieszMeasure Λ) K ≤ ENNReal.ofReal (Λ f)

If f assumes the value 1 on a compact set K then rieszMeasure K ≤ Λ f.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real

Cited by

3 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT2SpaceMeasurableSpaceBorelSpaceLocallyCompactSpace