measurable space
51Variable — A variable (pronEng|ˈvɛərɪəbl) is an attribute of a physical or an abstract system which may change its value while it is under observation. Examples include the height of a child, the temperature across a state, or the input to a function. This… …
52Ergodic measure — In mathematics, specifically in ergodic theory, an ergodic measure is a measure that satisfies the ergodic hypothesis for a given map of a measurable space into itself. Intuitively, an ergodic measure is one with respect to which the points of… …
53Regular conditional probability — is a concept that has developed to overcome certain difficulties in formally defining conditional probabilities for continuous probability distributions. It is defined as an alternative probability measure conditioned on a particular value of a… …
54Pushforward measure — In mathematics, a pushforward measure (also push forward or push forward) is obtained by transferring ( pushing forward ) a measure from one measurable space to another using a measurable function.DefinitionGiven measurable spaces ( X 1, Sigma;1) …
55Point process — In statistics and probability theory, a point process is a type of random process for which any one realisation consists of a set of isolated points either in time or geographical space, or in even more general spaces. For example, the occurrence …
56Support (measure theory) — In mathematics, the support (sometimes topological support or spectrum) of a measure μ on a measurable topological space ( X , Borel( X )) is a precise notion of where in the space X the measure lives . It is defined to be the largest (closed)… …
57Invariant measure — In mathematics, an invariant measure is a measure that is preserved by some function. Invariant measures are of great interest in the study of dynamical systems. The Krylov Bogolyubov theorem proves the existence of invariant measures under… …
58Simple function — In mathematical field of real analysis, a simple function is a real valued function over a subset of the real line which attains only a finite number of values. Some authors also require simple functions to be measurable; as used in practice,… …
59Filtration (mathematics) — In mathematics, a filtration is an indexed set Si of subobjects of a given algebraic structure S, with the index i running over some index set I that is a totally ordered set, subject to the condition that if i ≤ j in I then Si ⊆ Sj. The concept… …
60Random element — The term random element was introduced by Maurice Frechet in 1948 to refer to a random variable that takes values in spaces more general than had previously been widely considered. Frechet commented that the development of probability theory and… …
