measurable space
61Hahn decomposition theorem — In mathematics, the Hahn decomposition theorem, named after the Austrian mathematician Hans Hahn, states that given a measurable space ( X , Sigma;) and a signed measure mu; defined on the sigma; algebra Sigma;, there exist two sets P and N in… …
62Positive and negative sets — In measure theory, given a measurable space ( X , Sigma;) and a signed measure mu; on it, a set A isin; Sigma; is called a positive set for mu; if every Sigma; measurable subset of A has nonnegative measure; that is, for every E sube; A that… …
63Absolute continuity — In mathematics, the relationship between the two central operations of calculus, differentiation and integration, stated by fundamental theorem of calculus in the framework of Riemann integration, is generalized in several directions, using… …
64Adapted process — In the study of stochastic processes, an adapted process (or non anticipating process) is one that cannot see into the future . An informal interpretation[1] is that X is adapted if and only if, for every realisation and every n, Xn is known at… …
65Positive and negative parts — In mathematics, the positive part of a real or extended real valued function is defined by the formula Intuitively, the graph of f + is obtained by taking the graph of f, chopping off the part under the x axis, and letting f + take the value zero …
66Essential range — In mathematics, particularly measure theory, the essential range of a function is intuitively the non negligible range of the function. One way of thinking of the essential range of a function is the set on which the range of the function is most …
67Operator algebra — In functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings. Although it is usually classified as a branch of functional… …
68Convergence of measures — In mathematics, more specifically measure theory, there are various notions of the convergence of measures. Three of the most common notions of convergence are described below. Contents 1 Total variation convergence of measures 2 Strong… …
69Realization (probability) — In probability and statistics, a realization, or observed value, of a random variable is the value that is actually observed (what actually happened). The random variable itself should be thought of as the process how the observation comes about …
70Singular measure — In mathematics, two positive (or signed or complex) measures μ and ν defined on a measurable space (Ω, Σ) are called singular if there exist two disjoint sets A and B in Σ whose union is Ω such that μ is zero on all measurable subsets of B while… …
