= Pointwise separable function class
A measurable-function class is pointwise separable if it has a countable subclass such that every member is the pointwise limit of a sequence from that subclass. With an integrable common envelope, <dominated convergence theorem> makes both empirical averages and population expectations converge along each such sequence. Thus the supremum of the absolute empirical errors equals the supremum over the countable subclass and is measurable. A finite integrable bracketing cover provides an integrable envelope by taking the maximum absolute value of all its endpoints.
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