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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. [1]

9 relations: Blumenthal's zero–one law, Borel–Cantelli lemma, Doob's martingale convergence theorems, Engelbert–Schmidt zero–one law, Hewitt–Savage zero–one law, Kolmogorov's zero–one law, Markov chain, Meagre set, Probability theory.

Blumenthal's zero–one law

In the mathematical theory of probability, Blumenthal's zero–one law, named after Robert McCallum Blumenthal, is a statement about the nature of the beginnings of memoryless processes.

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Borel–Cantelli lemma

In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events.

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Doob's martingale convergence theorems

In mathematicsspecifically, in the theory of stochastic processesDoob's martingale convergence theorems are a collection of results on the long-time limits of supermartingales, named after the American mathematician Joseph L. Doob.

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Engelbert–Schmidt zero–one law

The Engelbert–Schmidt zero–one law is a theorem that gives a mathematical criterion for an event associated with a continuous, non-decreasing additive functional of Brownian motion to have probability either 0 or 1, without the possibility of an intermediate value.

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Hewitt–Savage zero–one law

The Hewitt–Savage zero–one law is a theorem in probability theory, similar to Kolmogorov's zero–one law and the Borel–Cantelli lemma, that specifies that a certain type of event will either almost surely happen or almost surely not happen.

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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, 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.

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Markov chain

A Markov chain is "a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event".

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Meagre set

In the mathematical fields of general topology and descriptive set theory, a meagre set (also called a meager set or a set of first category) is a set that, considered as a subset of a (usually larger) topological space, is in a precise sense small or negligible.

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Probability theory

Probability theory is the branch of mathematics concerned with probability.

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Redirects here:

0-1 law, 0-1 theorem, 0–1 law, Zero one law, Zero-one law, Zero-one law (disambiguation), Zero–one law (disambiguation).


[1] https://en.wikipedia.org/wiki/Zero–one_law

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