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 ?
Similar questions about the Hausdorff dimension of sets and measures are at the heart of geometric measure theory and we will establish Fourier analytic analogues of classical results in this direction.
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.
The question of whether the boundary behavior a general harmonic function can distinguish between a ball and a snowflake or between a Lipschitz domain and the complement of the 4-corner Cantor set illustrates the type of issues one is concerned with in this area of analysis, which lies at the interface of Partial Differential Equations, Harmonic Analysis, Geometric Measure Theory and Free Boundary Problems.
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.