Theorems · Theorem · measure theory

RealRMK.le_rieszMeasure_tsupport_subset

∀ {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 ∧ f x ≤ 1) → ∀ {V : Set X}, tsupport ⇑f ⊆ V → ENNReal.ofReal (Λ f) ≤ (RealRMK.rieszMeasure Λ) V

If f assumes values between 0 and 1 and the support is contained in V, then Λ f ≤ rieszMeasure V.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Real

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceT2SpaceMeasurableSpaceBorelSpaceLocallyCompactSpace