le_rieszMeasure_of_tsupport_subset

English

For compact K1 and K2 with disjointness, rieszContentAux Λ (K1 ⊔ K2) = rieszContentAux Λ K1 + rieszContentAux Λ K2.

Русский

Пусть K1 и K2 компактны и взаимно прерывны; тогда λ(K1 ∪ K2) = λ(K1) + λ(K2).

LaTeX

$$$\\lambda(K_{1}\\cup K_{2}) = λ(K_{1}) + λ(K_{2})$ when K1 ∩ K2 = ∅.$$

Lean4

theorem le_rieszMeasure_of_tsupport_subset {f : C_c(X, ℝ≥0)} (hf : ∀ x, f x ≤ 1) {V : Set X} (h : tsupport f ⊆ V) :
    .ofNNReal (Λ f) ≤ rieszMeasure Λ V := by
  apply le_trans _ (measure_mono h)
  apply le_rieszMeasure_of_isCompact_tsupport_subset Λ hf f.hasCompactSupport
  exact subset_rfl

Похожие утверждения