Sentence examples for basic theorem from inspiring English sources

A basic theorem says that there is a suitable σ-field containing all the intervals and a unique probability defined on this σ-field for which the probability of an interval is its length.

The basic theorem of information theory rests, first, upon the assumption that the message transmitted is well organized, consistent, and characterized by relatively low and determinable degrees of entropy and redundancy.

In addition, Dorflein [52] stated and proved that the basic theorem on coherence networks of concept lattices as an extension of the basic theorem on concept lattices.

Furthermore, these inequalities described above will be extended by this basic theorem.

In the study by Zhu in [1], a basic theorem is established and found to be a source of inequalities for circular functions, and these inequalities are extended by this basic theorem.

A basic theorem concerning the existence of the result and its uniqueness for the linear fractional equation is as follows.

In fact, all the basic theorems about limits and continuous functions followed from Dedekind's definition an outcome called the arithmetization of analysis.

In modern terms, Eudoxus' theory defined arbitrary magnitudes as limits of rational magnitudes, and basic theorems about the sum, difference, and product of magnitudes were equivalent to theorems about the sum, difference, and product of limits.

His best-known work concerned the analytic representation of a single-valued function; this work culminated in the Mittag-Leffler theorem, one of the basic theorems in analytic function theory.

One philosophical feature of traditional analysis, which worries mathematicians whose outlook is especially concrete, is that many basic theorems assert the existence of various numbers or functions but do not specify what those numbers or functions are.

Section 2 gives the basic theorems of fractional calculus.