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ℒ denotes the Lebesgue measurable subsets of ℝ and ${ℒ}_0$ denotes the sets of Lebesgue measure 0. In 1914 Burstin showed that a set M ⊆ ℝ belongs to ℒ if and only if every perfect P ∈ ℒ$ℒ0$hasaperfectsubsetQ\in ℒ\${ℒ}_0$ which is a subset of or misses M (a similar statement omitting “is a subset of or” characterizes ${ℒ}_0$). In 1935, Marczewski used similar language to define the σ-algebra (s) which we now call the “Marczewski measurable sets” and the σ-ideal $\left(s^0\right)$ which we call the “Marczewski null sets”. M ∈ (s) if every perfect set P has...