Zero–one law

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,
• Gaussian process § Driscoll's zero-one law.

Outside the area of probability, it may refer to:

• Topological zero–one law, related to meager sets,
• Zero-one law (logic) for sentences valid in finite structures.