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In [[Measure (mathematics)|measure theory]] and [[Probability theory|probability]], the '''monotone class theorem''' connects monotone classes and [[sigma-algebra]]s. The theorem says that the smallest monotone class containing an [[field of sets|algebra of sets]] ''G'' is precisely the smallest [[Sigma-algebra|''σ''-algebra]] containing ''G''. It is used as a type of [[transfinite induction]] to prove many other theorems, such as [[Fubini's theorem]].
==Definition of a monotone class==
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