Probability Theory

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 surely not happen; that is, the probability of such an event occurring is zero or one.

Cramér's theorem is a fundamental result in the theory of large deviations, a subdiscipline of probability theory.

In probability theory, Lindeberg's condition is a sufficient condition (and under certain conditions also a necessary condition) for the central limit theorem (CLT) to hold for a sequence of independent random variables.

In probability theory, the central limit theorem (CLT) states that

In probability theory, Bayes' theorem (alternatively Bayes' law or

In the theory of probability, the Glivenko-Cantelli theorem (sometimes referred

In probability theory, the de Moivre-Laplace theorem, which is a special

In probability theory, Chebyshev's inequality (also called the Bienaymé-Chebyshev

In probability theory, Markov's inequality gives an upper bound on

in measure theory. It is often stated in the context of probability theory, where it is used to study whether, in a given

In probability theory, Slutsky's theorem extends some properties of

In probability theory, Hoeffding's inequality provides an upper bound

In probability theory, Lévy's continuity theorem, or Lévy's convergence

In probability theory, de Finetti's theorem states that exchangeable

In probability theory, the central limit theorem states that, under

a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently

In probability theory, a Chernoff bound is an exponentially decreasing

In probability theory, Kolmogorov's three-series theorem, named after

from a given probability distribution. In the language of large deviations theory, Sanov's theorem identifies the rate function

In probability theory, Le Cam's theorem, named after Lucien Le Cam

In probability theory, Azuma's inequality or the Azuma-Hoeffding inequality

In mathematics, Varadhan's lemma is a result from the large deviations theory named after S. R. Srinivasa Varadhan.

The Hewitt-Savage zero-one law is a theorem in probability theory, similar to Kolmogorov's zero-one law and the

In probability theory, Cantelli's inequality (also called the Chebyshev-Cantelli

In probability theory, the coupon collector's problem refers to mathematical

In probability theory, the continuous mapping theorem states that continuous

theorem or the Cramér-Wold device is a theorem in measure theory and which states that a Borel probability measure

In probability theory, Kolmogorov's inequality is a so-called "maximal

In probability theory, Wald's equation, Wald's identity or Wald's lemma