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...

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...

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

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

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

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...

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

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...

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

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, 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...

linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical...

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...

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

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

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...

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

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

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...

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...

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

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...

given two measurable spaces and measures on them, one can obtain a product measurable space and a product measure on that space. Conceptually, this is...

"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...