Sentence examples for theory of measures from inspiring English sources

It organizes Lebesgue's theory of measures (described in the section Measure theory).

Although this sounds simple, the mathematical theory of measures is rather involved.

The theory of measures of noncompactness has many applications on topology, functional analysis, and operator theory.

The theory of measures of noncompactness can be found in the book of Akhmerov et al. [25] and in the book of Banaś and Goebel [26].

Using the theory of measures of noncompactness and applying a new method, we prove the existence of nondecreasing solutions of a quadratic integral equation of Volterra type in C(I).

González and Jiménez-Melado [3] used a fixed-point theorem derived from the theory of measures of noncompactness to investigate the existence of solutions for the second order difference equation Delta (q_{n}Delta x_{n} )+f_{n}(x_{n})=0, quad nge0.

In 1918 he published a set theory, the following year a theory of measure, and by 1923 a theory of functions, all developed without using the principle of the excluded middle.

It turns out to be simpler, however, not only to use Lebesgue's theory of measure to define probabilities but also to use his theory of integration to define expectation.

He later expanded the most important of these papers, "General Theory of Measure and Probability Theory"—which aimed to develop a rigorous, axiomatic foundation for probability into an influential monograph Grundbegriffe der Wahrscheinlichkeitsrechnung (1933; Foundations of the Theory of Probability, 1950).

The theory of measuring structural vibration using high-resolution images is presented first, based on sub-pixel edge identification.

We will use the theory of measure of noncompactness and a fixed point theorem of Darbo type to establish a new existence theorem for the problem (1.1 - 1.2 1.1 - 1.2