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Vector measure

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  • Vector measure — In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. Definitions and first consequencesGiven a field of sets (Omega, mathcal F) and a Banach space X, a finitely… …   Wikipedia

  • 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

  • Vector soliton — Among all the soliton considered, the optical soliton draws the most attention as it is possible to generate ultrafast pulses and has wider application. optical soliton can be classified as two groups:temporal soliton and spatial soliton.however …   Wikipedia

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

  • vector — vectorial /vek tawr ee euhl, tohr /, adj. vectorially, adv. /vek teuhr/, n. 1. Math. a. a quantity possessing both magnitude and direction, represented by an arrow the direction of which indicates the direction of the quantity and the length of… …   Universalium

  • vector analysis — the branch of calculus that deals with vectors and processes involving vectors. * * * ▪ mathematics Introduction       a branch of mathematics that deals with quantities that have both magnitude and direction. Some physical and geometric… …   Universalium

  • Vector magnetograph — A vector magnetograph is a type of imaging telescope that can estimate the 3 D vector of the magnetic field on a distant body with a resolved line spectrum. Magnetographs are useful for studying the Sun because the surface magnetic field is… …   Wikipedia

  • Measure of non-compactness — In functional analysis, two measures of non compactness are commonly used; these associate numbers to sets in such a way that compact sets all get the measure 0, and other sets get measures that are bigger according to how far they are removed… …   Wikipedia

  • Signed measure — In mathematics, signed measure is a generalization of the concept of measure by allowing it to have negative values. Some authors may call it a charge,[1] by analogy with electric charge, which is a familiar distribution that takes on positive… …   Wikipedia

  • Complex measure — In mathematics, specifically measure theory, a complex measure generalizes the concept of measure by letting it have complex values. In other words, one allows for sets whose size (length, area, volume) is a complex number. Contents 1 Definition… …   Wikipedia

  • Random measure — In probability theory, a random measure is a measure valued random element.Kallenberg, O., Random Measures , 4th edition. Academic Press, New York, London; Akademie Verlag, Berlin (1986). ISBN 0 123 94960 2 [http://www.ams.org/mathscinet… …   Wikipedia

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