Measure Theory

measure theory

[′mezh·ər ‚thē·ə·rē]
(mathematics)
The study of measures and their applications, particularly the integration of mathematical functions.

Measure Theory

 

a branch of mathematics that studies the property of measures of sets. Measure theory developed on the basis of works by M. E. C. Jordan, E. Borel, and, particularly, H. Lebesgue at the end of the 19th century and the beginning of the 20th. In these works, the concepts of length, area, and volume were extended beyond the class of figures usually considered in geometry. As a consequence, measures in their most general meaning (completely additive set functions) became the subject of measure theory. The development of measure theory is closely related to the development of the theory of the integral.

References in periodicals archive ?
building on recent pioneering work of the pi, The singularity project will investigate singularities through innovative strategies and tools that combine geometric measure theory with harmonic analysis.
Measure theory is becoming increasingly important in many fields, and the studies here focus on its application to non-smooth spaces within the realm of partial differential equations.
Appendices review partially ordered sets, Lebesgue measure theory, and mollifications.
Many papers on fuzzy sets have been appeared which shows the importance and its applications to set theory, algebra, real analysis, measure theory and topology etc.
3) allows us to treat the problem from the point of view of the measure theory on groups.
From the mathematical point of view, Shape Analysis and Stochastic Geometry use a variety of mathematical tools from differential geometry, geometric measure theory, stochastic processes, harmonic analysis, fractals, partial differential equations, etc.
These books raise the mathematical sophistication, and a full appreciation often requires prior advanced study in a number of areas including probability and measure theory, stochastic calculus, and differential equations.
This work presents theory and methods of statistical hypothesis testing based on measure theory, with emphasis on finding and evaluating appropriate statistical techniques.
Klir, Fhzzy Measure Theory, Plenum Press, New York, 1992.
To measure theory of mind, several false-related tasks were given to a sample of approximately 110 three- to five-year-old children.
This new insight was obtained when examining uncertainty by means of mathematical theories more general than classical set theory and classical measure theory.
Neither an appeal to infinitesimal probabilities nor a patch using standard measure theory avoids the difficulty.