lintegral_coeFn — Mathlib

English

For f,g ∈ α →ₘ[μ] γ, the coerced function of f/g equals the almost everywhere quotient: (f/g) cast equals f/g almost everywhere.

Русский

Для f,g ∈ α →ₘ[μ] γ, перевод функции f/g почти нигде совпадает с точечной дробью.

LaTeX

$$coeFn_div (f g : α →ₘ[μ] γ) : ⇑(f / g) =ᵐ[μ] f / g$$

Lean4

theorem lintegral_coeFn (f : α →ₘ[μ] ℝ≥0∞) : ∫⁻ a, f a ∂μ = f.lintegral := by
  rw [← lintegral_mk (hf := f.aestronglyMeasurable), mk_coeFn]

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