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Almost surely

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In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one. [1]

23 relations: Almost all, Almost everywhere, Asymptotic analysis, Brownian motion, Composite number, Connectivity (graph theory), Convergence of random variables, Degenerate distribution, Erdős–Rényi model, Event (probability theory), Independent and identically distributed random variables, Infinite monkey theorem, Infinite set, Law of large numbers, Measure (mathematics), Null set, Number theory, Prime number theorem, Probability space, Probability theory, Random graph, Sample space, 0.

Almost all

In mathematics, the term "almost all" means "all but a negligible amount".

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Almost everywhere

In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities.

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Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.

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Brownian motion

Brownian motion or pedesis (from πήδησις "leaping") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving molecules in the fluid.

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Composite number

A composite number is a positive integer that can be formed by multiplying together two smaller positive integers.

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Connectivity (graph theory)

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to disconnect the remaining nodes from each other.

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Convergence of random variables

In probability theory, there exist several different notions of convergence of random variables.

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Degenerate distribution

In mathematics, a degenerate distribution is a probability distribution in a space (discrete or continuous) with support only on a space of lower dimension.

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Erdős–Rényi model

In the mathematical field of graph theory, the Erdős–Rényi model is either of two closely related models for generating random graphs.

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Event (probability theory)

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

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Independent and identically distributed random variables

In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent.

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Infinite monkey theorem

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.

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Infinite set

In set theory, an infinite set is a set that is not a finite set.

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Law of large numbers

In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times.

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Measure (mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

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Null set

In set theory, a null set N \subset \mathbb is a set that can be covered by a countable union of intervals of arbitrarily small total length.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Prime number theorem

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.

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Probability space

In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that models a real-world process (or “experiment”) consisting of states that occur randomly.

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Probability theory

Probability theory is the branch of mathematics concerned with probability.

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Random graph

In mathematics, random graph is the general term to refer to probability distributions over graphs.

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Sample space

In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment.

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0

0 (zero) is both a number and the numerical digit used to represent that number in numerals.

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A.a.s., Almost always, Almost certain, Almost certainly, Almost never, Almost sure, Asymptotically almost surely, Impossible event, Probability 1, Probability of zero, Probability one, With probability 1, Zero probability.

References

[1] https://en.wikipedia.org/wiki/Almost_surely

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