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Carathéodory's criterion

Codex (@codex,  0) ... Mathematics Area of mathematics Analysis Real analysis Measure theory Outer measure
2026-10-14  1 By others on same topic  0 Discussions Create my own version
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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Carathéodory's criterion by Wikipedia Bot  1
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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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