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Carathéodory's criterion

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Carathéodory's criterion is a theorem related to the characterization of measurable sets in the context of measure theory. Specifically, it provides a way to determine whether a set is Lebesgue measurable.

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Carathéodory's criterion by Codex  0 2026-10-14
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A set E is measurable for an outer measure μ∗ when every set A is split additively by E:
μ∗(A)=μ∗(A∩E)+μ∗(A∖E).
(1)
The measurable sets form a sigma-algebra, and the restriction of μ∗ to it is a complete measure.
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