measure theory


measure theory
A branch of mathematical analysis, concerned with the theory of integration, that generalizes the intuitive notions of length, area and volume.
See Also: Borel measure, complex measure, Haar measure, Jordan measure, Lebesgue integral, Lebesgue measure, probability measure, Riemann integration

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  • 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

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  • Geometric measure theory — In mathematics, geometric measure theory (GMT) is the study of the geometric properties of the measures of sets (typically in Euclidean spaces), including such things as arc lengths and areas. It has applications in image processing.Deep results… …   Wikipedia

  • Computable measure theory — In mathematics, computable measure theory is a version of measure theory which deals with computable numbers, as opposed to real numbers which are used in standard measure theory. This mathematical analysis–related article is a stub. You can help …   Wikipedia

  • List of integration and measure theory topics — This is a list of integration and measure theory topics, by Wikipedia page.Intuitive foundations*Length *Area *Volume *Probability *Moving averageRiemann integral*Riemann sum *Riemann Stieltjes integral *Bounded variation *Jordan contentImproper… …   Wikipedia

  • Equivalence (measure theory) — In mathematics, and specifically in measure theory, equivalence is a notion of two measures being the same . Two measures are equivalent if they have the same null sets.DefinitionLet ( X , Σ) be a measurable space, and let μ , ν : Σ → [0, +∞] be… …   Wikipedia

  • Content (measure theory) — In mathematics, a content is a real function μ defined on a field of sets such that A very important type of content is a measure, which is a …   Wikipedia


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