In probability theory, a probability space or a probability triple ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} is a mathematical construct...

In probability theory, a standard probability space, also called Lebesgue–Rokhlin probability space or just Lebesgue space (the latter term is ambiguous)...

In probability and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the...

axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a...

random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the...

In probability theory, the sample space (also called sample description space, possibility space, or outcome space) of an experiment or random trial is...

Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a...

mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often has the interpretation of time...

(\Omega ,F,P)} is a probability space, with sample space Ω {\displaystyle \Omega } , event space F {\displaystyle F} and probability measure P {\displaystyle...

measure must assign value 1 to the entire space. Intuitively, the additivity property says that the probability assigned to the union of two disjoint (mutually...

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption...

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. A single outcome...

variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs...

In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It...

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically...

In probability theory particularly in the Malliavin calculus, a Gaussian probability space is a probability space together with a Hilbert space of mean...

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

defined as a measurable function from a probability measure space (called the sample space) to a measurable space. This allows consideration of the pushforward...

are called transition probabilities. The process is characterized by a state space, a transition matrix describing the probabilities of particular transitions...

{\displaystyle \Sigma _{*}} and probability measure P {\displaystyle \mathbb {P} } if Σ∗ is a filtration of the underlying probability space (Ω, Σ,  P {\displaystyle...

"almost everywhere" in measure theory. In probability experiments on a finite sample space with a non-zero probability for each outcome, there is no difference...

spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space"...

In probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes...

Probability measure, a real-valued function on a probability space Probability mass function Probability distribution function (disambiguation) This disambiguation...

In probability theory, a tree diagram may be used to represent a probability space. A tree diagram may represent a series of independent events (such...

described or modeled by a mathematical construct known as a probability space. A probability space is constructed and defined with a specific kind of experiment...

more formal probability theory, a random variable is a function X defined from a sample space Ω to a measurable space called the state space. If an element...

A prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence...

likely. Event (probability theory) – In statistics and probability theory, set of outcomes to which a probability is assigned Sample space – Set of all...

a measure space is a probability space. A measurable space consists of the first two components without a specific measure. A measure space is a triple...