Caratheodory measure

См. также в других словарях:

• Carathéodory's criterion — is a result in measure theory that was formulated by Greek mathematician Constantin Carathéodory. Its statement is as follows: Let lambda^* denote the Lebesgue outer measure on mathbb{R}^n, and let Esubseteqmathbb{R}^n. Then E is Lebesgue… …   Wikipedia

• Carathéodory's extension theorem — See also Carathéodory s theorem for other meanings. In measure theory, Carathéodory s extension theorem proves that for a given set Ω, you can always extend a sigma; finite measure defined on R to the sigma; algebra generated by R , where R is a… …   Wikipedia

• Carathéodory's theorem — In mathematics, Carathéodory s theorem may refer to one of a number of results of Constantin Carathéodory:* Carathéodory s theorem (convex hull) about the convex hulls of sets in Euclidean space *Carathéodory s theorem (measure theory) about… …   Wikipedia

• Carathéodory, Constantin — ▪ German mathematician born Sept. 13, 1873, Berlin, Ger. died Feb. 2, 1950, Munich       German mathematician of Greek origin who made important contributions to the theory of real functions, to the calculus of variations, and to the theory of… …   Universalium

• Measure (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 …   Wikipedia

• Constantin Carathéodory — Born 13 September 1873 …   Wikipedia

• Outer measure — In mathematics, in particular in measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. A general theory… …   Wikipedia

• Théorème d'extension de Carathéodory —  Ne pas confondre avec le théorème de Carathéodory en géométrie. En théorie de la mesure, le théorème d extension de Carathéodory est un théorème fondamental, qui est à la base de la construction de la plupart des mesures usuelles. Constitué …   Wikipédia en Français

• Lebesgue measure — In mathematics, the Lebesgue measure, named after Henri Lebesgue, is the standard way of assigning a length, area or volume to subsets of Euclidean space. It is used throughout real analysis, in particular to define Lebesgue integration. Sets… …   Wikipedia

• Hausdorff measure — In mathematics a Hausdorff measure is a type of outer measure, named for Felix Hausdorff, that assigns a number in [0,∞] to each set in R n or, more generally, in any metric space. The zero dimensional Hausdorff measure is the number of points in …   Wikipedia

• Doubling measure — In mathematics, a metric space X with metric d is said to be doubling if there is some constant M > 0 such that for any x in X and r > 0, the ball B(x, r) = {y:|x − y| < r} may be… …   Wikipedia