measure on intervals

measure — measurer, n. /mezh euhr/, n., v., measured, measuring. n. 1. a unit or standard of measurement: weights and measures. 2. a system of measurement: liquid measure. 3. an instrument, as a graduated rod or a container of standard capacity, for… …   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

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 zero — Math. the property of a set of points for which, given any small number, there exists a set of intervals such that each point of the given set is contained in at least one of the intervals and such that, essentially, the combined length of the… …   Universalium

measure zero — Math. the property of a set of points for which, given any small number, there exists a set of intervals such that each point of the given set is contained in at least one of the intervals and such that, essentially, the combined length of the… …   Useful english dictionary

measure theory — In mathematics, a generalization of the concepts of length and area (see length, area, and volume) to arbitrary sets of points not composed of line segments or rectangles. A measure is any rule for associating a number with a set. The result must …   Universalium

Jordan 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… …   Wikipedia

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

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

Klee's measure problem — In computational geometry, Klee s measure problem is the problem of determining how efficiently the measure of a union of (multidimensional) rectangular ranges can be computed. Here, a d dimensional rectangular range is defined to be a cartesian… …   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