lintegral_mul_const'' — Mathlib

English

For ENNReal r and Measurable f, ∫⁻ f a * r = (∫⁻ f a) * r.

Русский

Для ENNReal r и измеримой f: ∫⁻ f a · r = (∫⁻ f a) · r.

LaTeX

$$$\forall r : \mathbb{R}_{\ge 0}^{\infty},\; {f : α \to \mathbb{R}_{\ge 0}^{\infty}}\; (hf : AEMeasurable f μ) \Rightarrow ∫^- a, f a * r ∂μ = (∫^- a, f a ∂μ) * r$$$

Lean4

theorem lintegral_mul_const'' (r : ℝ≥0∞) {f : α → ℝ≥0∞} (hf : AEMeasurable f μ) :
    ∫⁻ a, f a * r ∂μ = (∫⁻ a, f a ∂μ) * r := by simp_rw [mul_comm, lintegral_const_mul'' r hf]

Похожие утверждения