∀ {α : Type u_1} [inst : PseudoEMetricSpace α] [inst_1 : MeasurableSpace α] [OpensMeasurableSpace α]
  {μ : MeasureTheory.Measure α} {s : Set α},
  (∃ R > 0, μ (Metric.cthickening R s) ≠ ⊤) →
    Filter.Tendsto (fun r => μ (Metric.cthickening r s)) (nhds 0) (nhds (μ (closure s)))