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# 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. [1]

## 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.

## Borel–Cantelli lemma

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

## 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.

## 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.

## 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.

## 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.

## 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".

## 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.

## Probability theory

Probability theory is the branch of mathematics concerned with probability.

## References

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