BIRKHOFF INTEGRAL IN QUASY-BANACH SPACES

Abstract

Aim of Investigation: Birkhoff integral of functions taking values in a Banach space plays an important role in the modern theory of integration (see [1],[4]). Therefore, it is with great interest the study of the existence of Birkhoff integral for the class of functions with values in a quasy – Banach space, and the properties of the Birkoff integral’s in this case. The other aim of this paper is analysis of validity of some of the known theorems for integration theory, at of Birkoff integral’s case.
Conclusions: The extension of the meaning of the Birkhoff integral, for functions with values in quasy – Banach space, together with the meanings of Aumann and Bochner integrals, allows us to see the class of functions with values in quasy -Banach spaces with a lot of interest in terms of integration.