Measurable
61Lebesgue integration — In mathematics, the integral of a non negative function can be regarded in the simplest case as the area between the graph of that function and the x axis. Lebesgue integration is a mathematical construction that extends the integral to a larger… …
62Sigma-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… …
63Space (mathematics) — This article is about mathematical structures called spaces. For space as a geometric concept, see Euclidean space. For all other uses, see space (disambiguation). A hierarchy of mathematical spaces: The inner product induces a norm. The norm… …
64Null set — In mathematics, a null set is a set that is negligible in some sense. For different applications, the meaning of negligible varies. In measure theory, any set of measure 0 is called a null set (or simply a measure zero set). More generally,… …
65Conditional 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… …
66Hölder's inequality — In mathematical analysis Hölder s inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of Lp spaces. Let (S, Σ, μ) be a measure space and let 1 ≤ p, q ≤ ∞ with… …
67Jordan measure — In mathematics, the Jordan measure (also known as the Jordan content) is an extension of the notion of size (length, area, volume) to shapes more complicated than, for example, a triangle, disk, or parallelipiped. It turns out that for a set to… …
68Monotone convergence theorem — In mathematics, there are several theorems dubbed monotone convergence; here we present some major examples. Contents 1 Convergence of a monotone sequence of real numbers 1.1 Theorem 1.2 Proof 1.3 …
69Radon–Nikodym theorem — In mathematics, the Radon–Nikodym theorem is a result in functional analysis that states that, given a measurable space ( X , Sigma;), if a sigma finite measure nu; on ( X , Sigma;) is absolutely continuous with respect to a sigma finite measure… …
70Determinacy — Determined redirects here. For the 2005 heavy metal song, see Determined (song). For other uses, see Indeterminacy (disambiguation). In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other… …
