∀ {X : Type u_2} [inst : EMetricSpace X] [inst_1 : MeasurableSpace X] [inst_2 : BorelSpace X] (m : ENNReal → ENNReal)
  (s : Set X),
  (MeasureTheory.Measure.mkMetric m) s =
    ⨆ r,
      ⨆ (_ : 0 < r),
        ⨅ t,
          ⨅ (_ : s ⊆ Set.iUnion t),
            ⨅ (_ : ∀ (n : ℕ), Metric.ediam (t n) ≤ r), ∑' (n : ℕ), ⨆ (_ : (t n).Nonempty), m (Metric.ediam (t n))