∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : TopologicalSpace β] [inst_2 : CompleteLattice β]
  [OrderClosedTopology β] [inst_4 : Zero β] [inst_5 : MeasurableSpace β] [OpensMeasurableSpace β] (i : ℕ → β)
  (f : α → β) (a : α),
  Measurable f → 0 = ⊥ → ⨆ n, (MeasureTheory.SimpleFunc.approx i f n) a = ⨆ k, ⨆ (_ : i k ≤ f a), i k