Applications of Generalized Measure Theory

  • Zhenyuan Wang
  • George J. Klir
Part of the IFSR International Series on Systems Science and Engineering book series (IFSR, volume 25)

General Remarks

It is undeniable that classical measure theory, based on additive measures and signed additive measures, and the associated Lebesgue theory of integration, is not only an important area of mathematics, but it has also played an important role in many application domains. Perhaps its most visible is its crucial role in probability theory, as rigorously formulated by Kolmogorov. Examples of other notable applications of classical measure theory are in the areas of classical geometry as well as fractal geometry, ergodic theory of dynamical systems, harmonic analysis, potential theory, calculus of variations, and mathematical economics (see Note 15.1).

Notwithstanding the many demonstrated applications of classical measure theory, it has increasingly been recognized that a broadening of this area’s applicability is severely limited by the additivity requirement of classical measures. Requiring additivity in measuring a property on sets of some kind is basically the same as...


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.University of Nebraska at OmahaOmahaUSA
  2. 2.Binghamton UniversityBinghamtonUSA

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