Category
page 1Theorems in probability theory
Bayes' theorem
theorem describing the probability of an event based on prior knowledge of conditions that might be related to the event
law of large numbers
theorem that describes the result of performing the same experiment a large number of times
infinite monkey theorem
humorously stated theorem that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will surely type a given text, such as the complete works of William Shakespeare.
central limit theorem
key theorem in probability theory
law of total probability
formula expressing the probability of an event in terms of its conditional probabilities over a partition of the sample space
Borel–Cantelli lemma
mathematical sentence
dominated convergence theorem
theorem that, for a sequence of functions bounded in absolute value by an integrable function, then almost everywhere pointwise convergence implies L¹ convergence
coupon collector's problem
probability Theory
Itō's lemma
identity in Itô calculus analogous to the chain rule
Kolmogorov's zero-one law
special case in probability theory; introduces tail events
Slutsky's theorem
theorem in probability theory
Bertrand's ballot theorem
theorem that, in an election where candidate A receives 𝑝 votes and candidate B receives 𝑞 votes (𝑝>𝑞), the probability that A will be strictly ahead of B throughout the count is (𝑝−𝑞)/(𝑝+𝑞)
Condorcet's jury theorem
political science theorem
Poisson limit theorem
probability theory
Wiener–Khinchin theorem
spectral decomposition theorem of stationary processes' autocorrelations
Lévy's continuity theorem
result in probability theory
optional stopping theorem
martingale's expected value at a stopping time equals its initial expected value
Lovász local lemma
lemma proving that a set of events with limited dependence has positive probability of all happening together
Glivenko–Cantelli theorem
theorem
de Finetti's theorem
theorem that exchangeable observations are conditionally independent relative to some latent variable
Karhunen–Loève theorem
theory of stochastic processes
Kolmogorov's three-series theorem
concept in probability theory
Skorokhod's representation theorem
theorem
Cox's theorem
theorem that derivates of the laws of probability from a certain set of postulates
Le Cam's theorem
probability theorem
Donsker's theorem
Statement in probability theory
Continuous Mapping Theorem
probability theorem
Hadwiger's theorem
theorem in integral geometry
Cramér–Wold theorem
theorem in measure theory
Kolmogorov's two-series theorem
probability theory
Hewitt–Savage zero–one law
theorem in probability theory
Gleason's theorem
theorem giving a justification of the Born rule in quantum mechanics
Reflection principle
result about the distribution of the supremum of a Brownian motion
Aumann's agreement theorem
theorem in game theory about whether rational agents can agree to disagree
Maxwell's theorem
concept in probability theory
Tanaka's formula
kind of differential equation
Krylov–Bogolyubov theorem
theorem