Measure Theory

measure theory

[′mezh·ər ‚thē·ə·rē]
(mathematics)
The study of measures and their applications, particularly the integration of mathematical functions.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
They do not justify the assignment of probabilities to propositions, and they might not be able to raise reasonable objections to speaking of the areas or volumes of propositions, since the probability theory is but an application of measure theory, a chapter of abstract mathematics.
He taught the Mathematical Analysis course for the first year students, and the Measure Theory course for the last year students.
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.
The formula (2.3) 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.