In
probability theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
, 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
In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli, who gave statement to the lemma in the first d ...
,
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Blumenthal's zero–one law for
Markov process
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, ...
es,
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Engelbert–Schmidt zero–one law for continuous, nondecreasing additive functionals of Brownian motion,
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Hewitt–Savage zero–one law for exchangeable sequences,
*
Kolmogorov's zero–one law
In probability theory, Kolmogorov's zero–one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, namely a ''tail event of independent σ-algebras'', will either almost surely happen or almost su ...
for the tail σ-algebra,
*
Lévy's zero–one law
In mathematicsspecifically, in the theory of stochastic processesDoob's martingale convergence theorems are a collection of results on the limits of supermartingales, named after the American mathematician Joseph L. Doob. Informally, the martin ...
, related to martingale convergence,
* .
Outside the area of probability, it may refer to:
* Topological zero–one law, related to
meager set
In the mathematical field of general topology, a meagre set (also called a meager set or a set of first category) is a subset of a topological space that is small or negligible in a precise sense detailed below. A set that is not meagre is called ...
s,
*
Zero-one law (logic) for sentences valid in finite structures.
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Probability theory