Theorems · Theorem · measure theory

rieszContentAux_image_nonempty

∀ {X : Type u_1} [inst : TopologicalSpace X] (Λ : CompactlySupportedContinuousMap X NNReal →ₗ[NNReal] NNReal)
  [T2Space X] [LocallyCompactSpace X] (K : TopologicalSpace.Compacts X), (⇑Λ '' {f | ∀ x ∈ K, 1 ≤ f x}).Nonempty

For any compact subset K ⊆ X, there exist some compactly supported continuous nonnegative functions f on X such that f ≥ 1 on K.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Basic

Cited by

3 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT2SpaceLocallyCompactSpace