Theorems · Theorem · measure theory

rieszContentAux_mono

∀ {X : Type u_1} [inst : TopologicalSpace X] (Λ : CompactlySupportedContinuousMap X NNReal →ₗ[NNReal] NNReal)
  [T2Space X] [LocallyCompactSpace X] {K₁ K₂ : TopologicalSpace.Compacts X},
  K₁ ≤ K₂ → rieszContentAux Λ K₁ ≤ rieszContentAux Λ K₂

Riesz content λ (associated with a positive linear functional Λ) is monotone: if K₁ ⊆ K₂ are compact subsets in X, then λ(K₁) ≤ λ(K₂).

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Basic

Cited by

3 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT2SpaceLocallyCompactSpace