∀ {ι : Type u_1} {u : Set ι} {p : ↑unitInterval} (S : Set (Set ι)),
  (ProbabilityTheory.setBernoulli u p) S =
    (MeasureTheory.Measure.infinitePi fun i =>
        unitInterval.toNNReal p • MeasureTheory.Measure.dirac (i ∈ u) +
          unitInterval.toNNReal (unitInterval.symm p) • MeasureTheory.Measure.dirac False)
      ((fun p => {i | p i}) ⁻¹' S)