measurable space
31Sample space — In probability theory, the sample space or universal sample space, often denoted S , Ω, or U (for universe ), of an experiment (probability theory) or random trial is the set of all possible outcomes. For example, if the experiment is tossing a… …
32Completely uniformizable space — In mathematics, a topological space (X, T) is called completely uniformizable (or Dieudonné complete or topologically complete) if there exists at least one complete uniformity that induces the topology T. Some authors additionally require X to… …
33Integral representation theorem for classical Wiener space — In mathematics, the integral representation theorem for classical Wiener space is a result in the fields of measure theory and stochastic analysis. Essentially, it shows how to decompose a function on classical Wiener space into the sum of its… …
34Lebesgue measurable — adjective That it is an element of the domain of the Lebesgue measure of the ambient Euclidean space …
35Measure (mathematics) — Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. In mathematical analysis …
36Direct integral — In mathematics and functional analysis a direct integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was… …
37Sigma-algebra — In mathematics, a σ algebra (also sigma algebra, σ field, sigma field) is a technical concept for a collection of sets satisfying certain properties. The main use of σ algebras is in the definition of measures; specifically, the collection of… …
38Conditional expectation — In probability theory, a conditional expectation (also known as conditional expected value or conditional mean) is the expected value of a real random variable with respect to a conditional probability distribution. The concept of conditional… …
39Field of sets — Set algebra redirects here. For the basic properties and laws of sets, see Algebra of sets. In mathematics a field of sets is a pair where X is a set and is an algebra over X i.e., a non empty subset of the power set of X closed under the… …
40Random variable — A random variable is a rigorously defined mathematical entity used mainly to describe chance and probability in a mathematical way. The structure of random variables was developed and formalized to simplify the analysis of games of chance,… …
