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

  • Valuation (measure theory) — In measure theory or at least in the approach to it through domain theory, a valuation is a map from the class of open sets of a topological space to the set positive real numbers including infinity. It is a concept closely related to that of a… …   Wikipedia

  • Information theory and measure theory — Measures in information theory = Many of the formulas in information theory have separate versions for continuous and discrete cases, i.e. integrals for the continuous case and sums for the discrete case. These versions can often be generalized… …   Wikipedia

  • Fuzzy measure theory — considers a number of special classes of measures, each of which is characterized by a special property. Some of the measures used in this theory are plausibility and belief measures, fuzzy set membership function and the classical probability… …   Wikipedia

  • 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

  • Atom (measure theory) — In mathematics, more precisely in measure theory, an atom is a measurable set which has positive measure and contains no set of smaller but positive measure. A measure which has no atoms is called non atomic or atomless. Contents 1 Definition 2… …   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

  • 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

  • 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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