ABSTRACT
formulates the approach to constructing a signal space on the basis of generalized Boolean algebra with a measure. The notion of information carrier space is defined. Chapter 2 considers main relationships between the elements of metric space built upon generalized Boolean algebra with a measure. The notions of main geometric objects of such metric space are defined. Axiomatic system of metric space built upon generalized Boolean algebra with a measure is formulated. This axiomatic system implies that the axioms of connection and the axioms of parallels are characterized with essentially the lesser constraints than the axioms of analogous groups of Euclidean space. It is shown that geometry of generalized Boolean algebra with a measure contains in itself some other known geometries. Chapter 2 establishes metric and trigonometrical relationships in space built upon generalized Boolean algebra with a measure. Chapter 2 investigates both geometric and algebraic properties of metric space built upon generalized Boolean algebra with a measure. Chapter 2 studies informational properties of such metric space. They are introduced axiomatically by the axiom of a measure of a binary operation of generalized Boolean algebra.
