hasFiniteIntegral_add_measure — Mathlib

English

If μ is finite and X in Icc[a,b] a.e., HasFiniteIntegral X μ.

Русский

Если μ конечна и X(a) ∈ Icc[a,b] почти всюду, HasFiniteIntegral X μ.

LaTeX

$$$[IsFiniteMeasure μ] \\Rightarrow (\\forall^{\\mathrm{a}} ω, X(ω) \\in \\mathrm{Icc}(a,b)) \\Rightarrow HasFiniteIntegral X μ$$$

Lean4

@[simp]
theorem hasFiniteIntegral_add_measure {f : α → ε} :
    HasFiniteIntegral f (μ + ν) ↔ HasFiniteIntegral f μ ∧ HasFiniteIntegral f ν :=
  ⟨fun h => ⟨h.left_of_add_measure, h.right_of_add_measure⟩, fun h => h.1.add_measure h.2⟩

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