# Zero–one law

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In probability theory, a **zero–one law** is a result that states that an event must have probability 0 or 1 and no intermediate value. Sometimes, the statement is that the limit of certain probabilities must be 0 or 1.

It may refer to:

- Borel–Cantelli lemma
- Blumenthal's zero–one law for Markov processes,
- Engelbert–Schmidt zero–one law for continuous, nondecreasing additive functionals of Brownian motion,
- Hewitt–Savage zero–one law for exchangeable sequences,
- Kolmogorov's zero–one law for the tail σ-algebra,
- Lévy's zero–one law, related to martingale convergence.
- Topological zero–one law, related to meager sets

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