mkMetric_top — Mathlib

English

The measure mkMetric with infinite bound equals the top measure: (mkMetric (fun _ => ∞) : Measure X) = ⊤.

Русский

Мера mkMetric с бесконечным пределом равна верхней мере: (mkMetric (функция, всегда бесконечность)) = ⊤.

LaTeX

$$$ (mkMetric (\text{fun } _ \Rightarrow ∞) : Measure X) = ⊤ $$$

Lean4

@[simp]
theorem mkMetric_top : (mkMetric (fun _ => ∞ : ℝ≥0∞ → ℝ≥0∞) : Measure X) = ⊤ :=
  by
  apply toOuterMeasure_injective
  rw [mkMetric_toOuterMeasure, OuterMeasure.mkMetric_top, toOuterMeasure_top]

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