Theorems · Theorem · measure theory

rieszContentAux_le

∀ {X : Type u_1} [inst : TopologicalSpace X] (Λ : CompactlySupportedContinuousMap X NNReal →ₗ[NNReal] NNReal)
  {K : TopologicalSpace.Compacts X} {f : CompactlySupportedContinuousMap X NNReal},
  (∀ x ∈ K, 1 ≤ f x) → rieszContentAux Λ K ≤ Λ f

Any compactly supported continuous nonnegative f such that f ≥ 1 on K gives an upper bound on the content of K; namely λ(K) ≤ Λ f.

Defined in

Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Basic

Cited by

2 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace