Abstract.The theory of hypernumbers is a novel approach in functional analysis aimed at the development of such mathematically correct technique, which allows operations with divergent integrals and series. Although, it resembles nonstandard analysis, there are several distinctions between these theories. For example, while nonstandard analysis changes spaces of real and complex numbers by injecting in to them infinitely small numbers and other nonstandard entities, the theory of extrafunctions does not change the inner structure of spaces of real and complex numbers, but adds to them infinitely big numbers as external objects. The goal of this paper is to develop the theory of hypermeasures in a sufficiently general context. To extend the scope of integration, we construct various kinds of hypermeasures. Hypermeasures similar to measures are set functions, only in contrast to measures, their values are not only numbers, but also arbitrary hypernumbers.

Received: June 5, 2005

AMS Subject Classification: 28B99

Key Words and Phrases: measure, hypernumber, hypermeasure, set ring, measurable set, linear space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 24
Issue: 3