= Solution
Use the exact-resource-balance convention for an <exchange economy>. If $\omega$ is the integrable initial-endowment profile, a feasible <consumption allocation> is a measurable integrable function $f:A\to\mathbb R_+^L$ with
$$
\int_Af\,d\mu=\int_A\omega\,d\mu.
$$
It is <Pareto efficient> if there is no other feasible <consumption allocation> $g$ satisfying $g(a)\succeq_a f(a)$ for almost every consumer and $g(a)\succ_a f(a)$ on a set of positive measure. \b[A Pareto improvement makes nobody worse off, up to a null set, and makes a positive-measure group strictly better off.] Positive measure is essential: reallocating to a single consumer of zero mass does not constitute an aggregate Pareto improvement.
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