Zero-one law
Encyclopedia
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:
Category:Probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, 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:
- Blumenthal's zero-one law for Markov processMarkov processIn probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time-varying random phenomenon for which a specific property holds...
es, - 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 lawKolmogorov's zero-one lawIn probability theory, Kolmogorov's zero-one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, called a tail event, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one.Tail...
for the terminal σ-algebra, - Lévy's zero-one law, related to martingale convergence.
Category:Probability theory