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definition of measure

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  • 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

  • Measure-preserving dynamical system — In mathematics, a measure preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Contents 1 Definition 2 Examples 3 Homomorphisms 4 …   Wikipedia

  • Measure algebra — In mathematics, a measure algebra is a Boolean algebra with a countably additive positive measure. A probability measure on a measure space gives a measure algebra on the Boolean algebra of measurable sets modulo null sets. Definition A measure… …   Wikipedia

  • Definition of music — How to define music has long been the subject of debate; philosophers, musicians, and, more recently, various social and natural scientists have argued about what constitutes music. The definition has varied through history, in different regions …   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

  • Perfect measure — In mathematics mdash; specifically, in measure theory mdash; a perfect measure (or, more accurately, a perfect measure space) is one that is ldquo;well behaved rdquo; in some sense. Intuitively, a perfect measure mu; is one for which, if we… …   Wikipedia

  • Oregon Ballot Measure 41 (2006) — Measure 41 Allows income tax deduction equal to Federal exemptions deduction to substitute for state exemption credit. Election results Yes or no …   Wikipedia

  • Radon measure — In mathematics (specifically, measure theory), a Radon measure, named after Johann Radon, is a measure on the σ algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular. Contents 1 Motivation 2 Definitions …   Wikipedia

  • Dynamical system (definition) — This article presents the many ways to define a dynamical system. See the main article, dynamical system, for an overview of the topic. The dynamical system concept is a mathematical formalization for any fixed rule which describes the time… …   Wikipedia

  • Support (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)… …   Wikipedia

  • Resource bounded measure — Lutz s resource bounded measure is a generalisation of Lebesgue measure to complexity classes. It was originally developed by Jack Lutz. Just as Lebesgue measure gives a method to quantify the size of subsets of the Euclidean space R^n, resource… …   Wikipedia

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